Approaches for beam selection

ABSTRACT

A method is disclosed for a system comprising a transmitter apparatus and a receiver apparatus. The transmitter apparatus is configured to transmit signals to the receiver apparatus using an available transmission beam. The receiver apparatus is configured to receive the signals using an available reception beam. The method comprises the transmitter apparatus determining a collection of linear combinations of transmission beams and a collection of linear combinations of reception beams, providing an indication of the collection of linear combinations of reception beams to the receiver apparatus and transmitting each of the linear combinations of transmission beams of the collection of linear combinations of transmission beams. The method also comprises the receiver apparatus acquiring the indication of the collection of linear combinations of reception beams from the transmitter apparatus, receiving each of the linear combinations of transmission beams of the collection of linear combinations of transmission beams using each of the linear combinations of reception beams of the collection of linear combinations of reception beams, and performing beam selection measurements on the received linear combinations of transmission beams for selection of the transmission beam from the plurality of available transmission beams and for selection of the reception beam from the plurality of available reception beams. Methods for each of the transmitter apparatus and the receiver apparatus are also disclosed, as well as corresponding apparatuses, network node, wireless communication device, system and computer program product.

TECHNICAL FIELD

The present disclosure relates generally to the field of wirelesscommunication. More particularly, it relates to approaches for beamselection in relation to beam forming applied in wireless communication.

BACKGROUND

In wireless communication standards that rely on bearnforming (e.g.,fifth generation (SG), new radio (NR), IEEE 802.11ay, etc.), animportant procedure for the base station (BS) is to find the best (or atleast a good enough) transmission beam towards each user equipment (UE)that it serves, and for each UE to find the best (or at least a goodenough) reception beam for reception from the BS. This is usuallyachieved by some type of training transmissions (also referred to asbeam training or beam sweeping).

One way to implement such a procedure (which is used in IEEE 802.11ac,for example) is to let the BS transmit orthogonal beams, and let the UEestimate—for each reception beam—the downlink (DL) channel and/orreceived signal-to-noise ratio (SNR) based on the transmission.

Then the UE can send reports to the BS indicative of the estimationand/or a desired beam selection determined based on the estimation. Thisprocess may be referred to as beam sweeping.

The number of orthogonal transmission beams that must be transmitted, aswell as the number of orthogonal reception beams that must be used forreception, in such a training implementation are, typically, in theorder of (e.g., equals or are at most equal to) the number of antennas(or antenna elements) at the BS multiplied by the number of antennas (orantenna elements) at the UE. Thus, this approach may be useful whenthere is a low or moderate number of antenna elements. However, forsituations with a large number of antenna elements (e.g., massivemultiple-input multiple-output, MIMO), the number of beams becomes largewhich makes this approach cumbersome. For example, a substantial amountof time may need to be allocated for the training transmissions andreceptions and the training contribute with a large amount of overheadsignaling, both of which may impair system capacity.

In such situations, the BS may instead transmit a lower number oftransmission beams than in the implementation referred to above; e.g.,beams of a transmission codebook that contains less than alltransmission beams and that preferably span as much as possible of theentire BS antenna space. This process may also be referred to as beamsweeping.

The UE may similarly use a lower number of reception beams than in theimplementation referred to above; e.g., beams of a reception codebookthat contains less than all possible reception beams and that preferablyspan as much as possible of the entire UE antenna space.

Thus, beam sweeping may be implemented such that the BS transmits on oneof the transmit beams of the transmission codebook at a time, and the UEreceives on one of the reception beam of the reception codebook at atime. Then, the UE may signal, to the BS, the index of the transmissionbeam that is part of the transmission/reception beam pair that achievesthe best performance as measured at the UE.

Even in this approach, however, the amount of time and/or signalingoverhead of the training may be substantial.

Therefore, there is a need for more efficient approaches for beamselection. Preferably, such approaches require less time allocationand/or less signaling overhead than other approaches. Also preferable,such approaches achieve the same results concerning beam selection(e.g., in terms of signal-to-noise ratio, SNR, when the selected beamsare used). If approaches achieve deteriorated results concerning beamselection, it is preferable that the deterioration is minimal, or atleast not substantial.

SUMMARY

It should be emphasized that the term “comprises/comprising”(replaceable by “includes/including”) when used in this specification istaken to specify the presence of stated features, integers, steps, orcomponents, but does not preclude the presence or addition of one ormore other features, integers, steps, components, or groups thereof. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise.

Generally, when an arrangement is referred to herein, it is to beunderstood as a physical product; e.g., an apparatus. The physicalproduct may comprise one or more parts, such as controlling circuitry inthe form of one or more controllers, one or more processors, or thelike.

It is an object of some embodiments to solve or mitigate, alleviate, oreliminate at least some of the above or other disadvantages.

A first aspect is a method for a transmitter apparatus configured totransmit signals to a receiver apparatus using a transmission beamselected from a plurality of available transmission beams, wherein thereceiver apparatus is configured to receive the signals using areception beam selected from a plurality of available reception beams. Aset of the available transmission beams and a set of the availablereception beams are for beam selection measurements by the receiverapparatus.

The method comprises determining a collection of linear combinations oftransmission beams of the set of the available transmission beams anddetermining a collection of linear combinations of reception beams ofthe set of available reception beams.

The method also comprises providing an indication of the collection oflinear combinations of reception beams to the receiver apparatus, andtransmitting each of the linear combinations of transmission beams ofthe collection of linear combinations of transmission beams for beamselection measurements by the receiver apparatus.

In some embodiments, the collection of linear combinations oftransmission beams and the collection of linear combinations ofreception beams are determined jointly.

In some embodiments, a cardinality of the collection of linearcombinations of transmission beams is lower than a cardinality of theset of the available transmission beams and/or a cardinality of thecollection of linear combinations of reception beams is lower than acardinality of the set of the available reception beams.

In some embodiments, the determination of the collection of linearcombinations of transmission beams and the collection of linearcombinations of reception beam comprises determining the cardinality ofthe collection of linear combinations of transmission beams and/or thecardinality of the collection of linear combinations of reception beambased on one or more of: a sparsity of a channel between the transmitterapparatus and the receiver apparatus, and properties of a compressionmatrix representing the collection of linear combinations oftransmission beams and the collection of linear combinations ofreception beams.

In some embodiments, the method further comprises receiving atransmission beam selection measurement report from the receiverapparatus, and selecting the transmission beam from the plurality ofavailable transmission beams in accordance with the receivedtransmission beam selection measurement report.

In some embodiments, at least one of the linear combinations oftransmission beams of the collection of linear combinations oftransmission beams is a linear combination of at least two of thetransmission beams of the set of the available transmission beams.

In some embodiments, at least one of the linear combinations ofreception beams of the collection of the collection of linearcombinations of reception beams is a linear combination of at least twoof the reception beams of the set of the available reception beams.

In some embodiments, each of the linear combinations of transmissionbeams of the collection of linear combinations of transmission beams isa unique linear combination of all of the transmission beams of the setof the available transmission beams.

In some embodiments, each of the linear combinations of reception beamsof the collection of the collection of linear combinations of receptionbeams is a unique linear combination of all of the reception beams ofthe set of the available reception beams.

In some embodiments, the collection of linear combinations oftransmission beams is defined by a Grassmannian coding matrix.

In some embodiments, the collection of linear combinations of receptionbeams is defined by a Grassmannian coding matrix.

In some embodiments, the collection of linear combinations oftransmission beams, representable by a matrix B_(TX), and the collectionof linear combinations of reception beams, representable by a matrixB_(RX), are determined such that A^(H)A is a substantially blockdiagonal matrix, wherein A=B_(TX)⊗B_(ax) where ⊗ represents a Kroneckerproduct.

In some embodiments, the set of the available transmission beamsconsists of a minimum number of transmission beams spanning theplurality of available transmission beams.

In some embodiments, the set of the available reception beams consistsof a minimum number of reception beams spanning the plurality ofavailable reception beams.

In some embodiments, the set of the available transmission beams and/orthe set of the available reception beams comprises discrete Fouriertransform (DFT) beams, wherein a beam direction of any DFT beamcorresponds to a harmonic frequency.

In some embodiments, transmitting each of the linear combinations oftransmission beams comprises one or more of: transmitting each of thelinear combinations of transmission beams of the collection of linearcombinations of transmission beams in a respective transmission timeresource (at least some of the respective time resources beingdifferent), and transmitting each of the linear combinations oftransmission beams of the collection of linear combinations oftransmission beams in a respective transmission frequency resource (atleast some of the respective frequency resources being different).

In some embodiments, the method is applied during a training phase forbeam selection.

An alternative to the first aspect is a method for a transmitterapparatus configured to transmit signals to a receiver apparatus using atransmission beam selected from a plurality of available transmissionbeams, wherein the receiver apparatus is configured to receive thesignals using a reception beam selected from a plurality of availablereception beams. A set of the available transmission beams and a set ofthe available reception beams are for beam selection measurements by thereceiver apparatus.

The method comprises determining a collection of linear combinations oftransmission beams of the set of the available transmission beams anddetermining a collection of linear combinations of reception beams ofthe set of available reception beams. The collection of linearcombinations of transmission beams and the collection of linearcombinations of reception beams are determined jointly.

The method also comprises, transmitting each of the linear combinationsof transmission beams of the collection of linear combinations oftransmission beams for beam selection measurements by the receiverapparatus.

In some embodiments, the method further comprises providing anindication of the collection of linear combinations of reception beamsto the receiver apparatus.

This alternative may additionally have features identical with orcorresponding to any of the various features as explained above for thefirst aspect.

Furthermore, this alternative is also applicable mutatis mutandis to theother aspects described in the following.

A second aspect is a method for a receiver apparatus configured toreceive signals from a transmitter apparatus via a transmission beamselected from a plurality of available transmission beams and using areception beam selected from a plurality of available reception beams. Aset of the available transmission beams and a set of the availablereception beams are for beam selection measurements by the receiverapparatus.

The method comprises acquiring, from the transmitter apparatus, anindication of a collection of linear combinations of reception beams ofthe set of the available reception beams.

The method also comprises receiving, using each of the linearcombinations of reception beams of the collection of linear combinationsof reception beams, a number of measurement signals for beam selectionmeasurements from the transmitter apparatus. The number of measurementsignals correspond to a collection of linear combinations oftransmission beams of the set of available transmission beams.

Furthermore, the method comprises performing beam selection measurementson the number of measurement signals for selection of the transmissionbeam from the plurality of available transmission beams and forselection of the reception beam from the plurality of availablereception beams.

In some embodiments, the method further comprises transmitting atransmission beam selection measurement report to the transmitterapparatus for selection of the transmission beam from the plurality ofavailable transmission beams.

In some embodiments, performing beam selection measurements comprisesdetermining a quality metric for each combination of a transmission beamof the set of available transmission beams and a reception beam of theset of available reception beams based on the beam selectionmeasurements.

In some embodiments, performing beam selection measurements comprisessubjecting the number of received measurement signals to matchedfiltering based on the collection of linear combinations of transmissionbeams and the collection of linear combinations of reception beam.

A third aspect is a method for a system comprising a transmitterapparatus and a receiver apparatus, wherein the transmitter apparatus isconfigured to transmit signals to the receiver apparatus using atransmission beam selected from a plurality of available transmissionbeams, and wherein the receiver apparatus is configured to receive thesignals using a reception beam selected from a plurality of availablereception beams. A set of the available transmission beams and a set ofthe available reception beams are for beam selection measurements by thereceiver apparatus.

The method comprises determining (by the transmitter apparatus) acollection of linear combinations of transmission beams of the set ofthe available transmission beams and a collection of linear combinationsof reception beams of the set of available reception beams.

The method also comprises providing (by the transmitter apparatus to thereceiver apparatus) an indication of the collection of linearcombinations of reception beams, and acquiring (by the receiverapparatus from the transmitter apparatus) the indication of thecollection of linear combinations of reception beams.

Furthermore, the method comprises transmitting (by the transmitterapparatus) each of the linear combinations of transmission beams of thecollection of linear combinations of transmission beams, and receiving(by the receiver apparatus) each of the linear combinations oftransmission beams of the collection of linear combinations oftransmission beams using each of the linear combinations of receptionbeams of the collection of linear combinations of reception beams.

The method also comprises performing (by the receiver apparatus) beamselection measurements on the received linear combinations oftransmission beams for selection of the transmission beam from theplurality of available transmission beams and for selection of thereception beam from the plurality of available reception beams.

A fourth aspect is a computer program product comprising anon-transitory computer readable medium, having thereon a computerprogram comprising program instructions. The computer program isloadable into a data processing unit and configured to cause executionof the method according to any of the first, second and third aspectswhen the computer program is run by the data processing unit.

A fifth aspect is a transmitter apparatus configured to transmit signalsto a receiver apparatus using a transmission beam selected from aplurality of available transmission beams, wherein the receiverapparatus is configured to receive the signals using a reception beamselected from a plurality of available reception beams. A set of theavailable transmission beams and a set of the available reception beamsare for beam selection measurements by the receiver apparatus.

The apparatus comprises controlling circuitry configured to causedetermination of a collection of linear combinations of transmissionbeams of the set of the available transmission beams, and determinationof a collection of linear combinations of reception beams of the set ofavailable reception beams.

The controlling circuitry is also configured to cause provision of anindication of the collection of linear combinations of reception beamsto the receiver apparatus, and transmission of each of the linearcombinations of transmission beams of the collection of linearcombinations of transmission beams for beam selection measurements bythe receiver apparatus.

The fifth aspect may be formulated as the transmitter apparatuscomprising a determiner, a provider, and a transmitter. The determineris configured to determine a collection of linear combinations oftransmission beams of the set of the available transmission beams, and acollection of linear combinations of reception beams of the set ofavailable reception beams. The provider is configured to provide anindication of the collection of linear combinations of reception beamsto the receiver apparatus. The transmitter is configured to transmiteach of the linear combinations of transmission beams of the collectionof linear combinations of transmission beams for beam selectionmeasurements by the receiver apparatus.

A sixth aspect is a receiver apparatus configured to receive signalsfrom a transmitter apparatus via a transmission beam selected from aplurality of available transmission beams and using a reception beamselected from a plurality of available reception beams. A set of theavailable transmission beams and a set of the available reception beamsare for beam selection measurements by the receiver apparatus.

The apparatus comprises controlling circuitry configured to causeacquisition, from the transmitter apparatus, of an indication of acollection of linear combinations of reception beams of the set of theavailable reception beams.

The controlling circuitry is also configured to cause reception, usingeach of the linear combinations of reception beams of the collection oflinear combinations of reception beams, of a number of measurementsignals for beam selection measurements from the transmitter apparatus.The number of measurement signals correspond to a collection of linearcombinations of transmission beams of the set of available transmissionbeams.

Furthermore, the controlling circuitry is configured to causeperformance of beam selection measurements on the number of measurementsignals for selection of the transmission beam from the plurality ofavailable transmission beams and for selection of the reception beamfrom the plurality of available reception beams.

The sixth aspect may be formulated as the receiver apparatus comprisingan acquirer, a receiver, and a measurer. The acquirer is configured toacquire, from the transmitter apparatus, an indication of a collectionof linear combinations of reception beams of the set of the availablereception beams. The receiver is configured to receive, using each ofthe linear combinations of reception beams of the collection of linearcombinations of reception beams, a number of measurement signals forbeam selection measurements from the transmitter apparatus. The numberof measurement signals correspond to a collection of linear combinationsof transmission beams of the set of available transmission beams. Themeasurer is configured to perform beam selection measurements on thenumber of measurement signals for selection of the transmission beamfrom the plurality of available transmission beams and for selection ofthe reception beam from the plurality of available reception beams.

A seventh aspect is a network node comprising the transmitter apparatusof the fifth aspect and/or the receiver apparatus of the sixth aspect.

An eighth aspect is a wireless communication device comprising thetransmitter apparatus of the fifth aspect and/or the receiver apparatusof the sixth aspect.

A ninth aspect is a system comprising a transmitter apparatus and areceiver apparatus, wherein the transmitter apparatus is configured totransmit signals to the receiver apparatus using a transmission beamselected from a plurality of available transmission beams, and whereinthe receiver apparatus is configured to receive the signals using areception beam selected from a plurality of available reception beams. Aset of the available transmission beams and a set of the availablereception beams are for beam selection measurements by the receiverapparatus.

The transmitter apparatus is configured to determine a collection oflinear combinations of transmission beams of the set of the availabletransmission beams and determine a collection of linear combinations ofreception beams of the set of available reception beams.

The transmitter apparatus is also configured to provide (to the receiverapparatus) an indication of the collection of linear combinations ofreception beams, and transmit each of the linear combinations oftransmission beams of the collection of linear combinations oftransmission beams.

The receiver apparatus is configured to acquire (from the transmitterapparatus) the indication of the collection of linear combinations ofreception beams, and receive each of the linear combinations oftransmission beams of the collection of linear combinations oftransmission beams using each of the linear combinations of receptionbeams of the collection of linear combinations of reception beams.

The receiver apparatus is also configured to perform beam selectionmeasurements on the received linear combinations of transmission beamsfor selection of the transmission beam from the plurality of availabletransmission beams and for selection of the reception beam from theplurality of available reception beams.

In some embodiments, any of the above aspects may additionally havefeatures identical with or corresponding to any of the various featuresas explained above for any of the other aspects.

An advantage of some embodiments is that alternative approaches for beamselection are provided.

The alternative approaches may, in some embodiments, be more efficientthan other approaches for beam selection. Efficiency may, for example,be in terms of the amount of time and/or signaling overhead needed forbeam training.

The alternative approaches may, in some embodiments, require lessresource (e.g., time and/or frequency) allocation and/or less signalingoverhead than other approaches for beam selection.

The alternative approaches may, in some embodiments, achieve beamselection that is not severely deteriorated compared to other approachesfor beam selection (e.g., in terms of resulting received SNR of theselected beam).

An advantage of some embodiments is that a significant reduction oftraining overhead for beam sweeping may be achieved at the cost of amarginal increase in error probability for detecting the bestcombination of transmission-reception beams.

Yet an advantage of some embodiments is that the amount of energyemitted in connection with the beam training may be reduced, therebyreducing interference generated for other wireless communications usingthe same communication medium.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects, features and advantages will appear from the followingdetailed description of embodiments, with reference being made to theaccompanying drawings. The drawings are not necessarily to scale,emphasis instead being placed upon illustrating the example embodiments.

FIG. 1A is a flowchart illustrating example method steps according tosome embodiments;

FIG. 1B is a flowchart illustrating example method steps according tosome embodiments;

FIG. 1C is a signaling diagram illustrating example signaling accordingto some embodiments;

FIGS. 2A and 2B are schematic block diagrams illustrating examplearrangements according to some embodiments;

FIGS. 3A and 3B are schematic block diagrams illustrating examplearrangements according to some embodiments;

FIG. 4 is a schematic drawing illustrating an example computer readablemedium according to some embodiments;

FIGS. 5A and 5B are simulation plots illustrating example resultsobtainable by application of some embodiments;

FIG. 6 illustrates a telecommunication network connected via anintermediate network to a host computer in accordance with someembodiments;

FIG. 7 illustrates a host computer communicating via a base station witha user equipment over a partially wireless connection in accordance withsome embodiments;

FIG. 8 is a flowchart illustrating example method steps implemented in acommunication system including a host computer, a base station and auser equipment in accordance with some embodiments;

FIG. 9 is a flowchart illustrating example method steps implemented in acommunication system including a host computer, a base station and auser equipment in accordance with some embodiments;

FIG. 10 is a flowchart illustrating example method steps implemented ina communication system including a host computer, a base station and auser equipment in accordance with some embodiments; and

FIG. 11 is a flowchart illustrating example method steps implemented ina communication system including a host computer, a base station and auser equipment in accordance with some embodiments.

DETAILED DESCRIPTION

As already mentioned above, it should be emphasized that the term“comprises/comprising” (replaceable by “includes/including”) when usedin this specification is taken to specify the presence of statedfeatures, integers, steps, or components, but does not preclude thepresence or addition of one or more other features, integers, steps,components, or groups thereof. As used herein, the singular forms “a”,an and “the” are intended to include the plural forms as well, unlessthe context clearly indicates otherwise.

Embodiments of the present disclosure will be described and exemplifiedmore fully hereinafter with reference to the accompanying drawings. Thesolutions disclosed herein can, however, be realized in many differentforms and should not be construed as being limited to the embodimentsset forth herein.

As mentioned above, the amount of time and/or signaling overhead of thetraining for beam forming selection may be substantial.

For example, if the BS is assumed to have a large antenna array (e.g.,64 antennas or more), the beam sweeping procedure typically consumesmany resources since there are many beams to transmit from the BS evenif only beams of a transmission codebook that contains less than alltransmission beams are included in the beam sweep. If the UE also has arelatively large reception codebook of reception beams, the beamsweeping procedure is even longer.

If N_(BS) denotes the number of transmission beams in the beam sweepingcodebook at the BS and N_(UE) denotes the number of reception beams inthe beam sweeping codebook at the UE, the beam sweeping trainingperformed in downlink (DL) comprises testing N_(BS)N_(UE) beamcombinations (and similarly for the uplink, UL). Clearly, if both N_(BS)and N_(UE) are large, the resulting product is also large.

Therefore, there is a need for more efficient approaches for beamselection. Such approaches may aim at reducing the number of beamcombinations that are tested in the beam sweeping, while achieving thesame, or only slightly inferior beam selection.

It should be noted that even though embodiments are described herein asused during a beam forming training period, it may (alternatively oradditionally) be equally applicable during other periods, e.g., duringperiods of data transmission.

In the following, embodiments will be described where alternativeapproaches for beam selection are provided.

FIG. 1A illustrates an example method 100 according to some embodiments,FIG. 1B illustrates an example method 100 according to some embodiments,and FIG. 1C illustrates example signaling according to some embodiments.The methods and the signaling may be applied only during a trainingphase for beam selection, according to some embodiments. Alternatively,the methods and the signaling may be applied during a training phase forbeam selection and during other periods, e.g., during periods of datatransmission. Yet alternatively, the methods and the signaling may beapplied only during periods other that the trading phase, e.g., duringperiods of data transmission.

The example method 100 is for a transmitter apparatus, the method 150 isfor a receiver apparatus, and the example signaling is between thetransmitter apparatus 190A and the receiver apparatus 190B. Thetransmitter apparatus is configured to transmit signals to the receiverapparatus using a transmission beam selected from a plurality ofavailable transmission beams. The receiver apparatus is configured toreceive signals from the transmitter apparatus via a transmission beamselected from a plurality of available transmission beams and using areception beam selected from a plurality of available reception beams.

Typically, the plurality of available transmission beams may compriseall possible beams for transmission from the transmitter apparatus, andthe plurality of available reception beams may comprise all possiblebeams for reception at the receiver apparatus.

A set of the available transmission beams and a set of the availablereception beams are for beam selection measurements by the receiverapparatus. Thus, these sets are the sets of beams used for beamtraining. The set may comprise all transmission/reception beams in theplurality of available transmission/reception beams or a subset of theplurality of available transmission/reception beams. In someembodiments, the beams of each of the sets are orthogonal, but this isnot necessarily true for all embodiments.

In some embodiments, the beams of each of the sets span a space whereall of the transmission/reception beams of the plurality of availabletransmission/reception beams reside. When used herein, the term“spanning a space” is meant to encompass any known and suitablemathematical definition of this term. Typically, each of the sets ofbeams consists of a minimum number of transmission/reception beamsspanning the plurality of available transmission/reception beams (i.e.,the space where all of the beams of the plurality of availabletransmission/reception beams reside). For example, the sets maycorrespond to the beam sweeping codebooks at the transmitter apparatusand at the receiver apparatus, respectively.

Each of the sets of the plurality of available transmission receptionbeams may, for example, comprise discrete Fourier transform (DFT) beams,wherein a beam direction of any beam in the set corresponds to aharmonic frequency. DFT beams can be constructed to span the wholeantenna space (e.g., by choosing harmonic frequencies of the DFT asangles for the beams), and they have constant amplitude on each antenna(which is desirable from a power amplifier (PA) point of view).

Moreover, the channel itself can typically be expressed as a weightedcombination of DFT beams with different angles. Due to this channeldecomposition property, some DFT beams are expected to be well alignedwith the channel, which makes them attractive from the perspectiveherein.

Thus, the beams in the BS and UE codebooks may be chosen as a DFT-likegrid of beams, uniformly spread in the azimuth plane. This choice ofbeams is particularly suitable since, typically, any MIMO channel can bedecomposed into a sum of DFT-like paths at certain (unknown) angles.Thus, by choosing this structure of the codebook beams at BS and UE tobe the same as the structure of the paths that constitute the MIMOchannel, it may be expected that some transmission and reception beamswill be well aligned with some of the paths.

In the following, techniques will be exemplified for reducing the numberof beams transmitted and/or received for training purposes, withoutsubstantial loss in performance of the selected beams.

In step 101 of method 100, a collection of linear combinations oftransmission beams of the set of the available transmission beams isdetermined, as well as a collection of linear combinations of receptionbeams of the set of the available reception beams.

Typically, the collection of linear combinations of transmission beamsand the collection of linear combinations of reception beams may bedetermined jointly. Joint determination may comprise determination in ajoint operation; such that the determination of the collection of linearcombinations of transmission beams depends on the collection of linearcombinations of reception beams, and/or such that the determination ofthe collection of linear combinations of reception beams depends on thecollection of linear combinations of transmission beams.

In some embodiments, one or more of the determinations of step 101 maybe specified, e.g., in a standard. Alternatively or additionally, theone or more of the determinations of step 101 may be based on a sparsityof the channel as experienced at the transmitter apparatus and/or at thereceiver apparatus (e.g., a sparsity of a channel between thetransmitter apparatus and the receiver apparatus). Yet alternatively oradditionally, the one or more of the determinations of step 101 may bebased on properties of a compression matrix representing the collectionof linear combinations of transmission beams and the collection oflinear combinations of reception beams.

The cardinality of the collection of linear combinations of transmissionbeams may be equal to, or lower than, the cardinality of the set of theavailable transmission beams. Similarly, the cardinality of thecollection of linear combinations of reception beams may be equal to, orlower than, the cardinality of the set of the available reception beams.The cardinalities of the collections are also larger than one.

Typically, at least one of the cardinality of the collection of linearcombinations of transmission beams and the cardinality of the collectionof linear combinations of reception beams is lower than the cardinalityof the respective set of the available transmission/reception beams. Insome embodiments, the cardinality of the collection of linearcombinations of transmission beams is lower than the cardinality of theset of the available transmission beams, and the cardinality of thecollection of linear combinations of reception beams is lower than thecardinality of the set of the available reception beams.

In some embodiments, one or more of the determinations of step 101 maycomprise determining the cardinality of the collection of linearcombinations of transmission and/or reception beams based on a sparsityof the channel as experienced at the transmitter apparatus and/or at thereceiver apparatus (e.g., a sparsity of a channel between thetransmitter apparatus and the receiver apparatus). Alternatively oradditionally, one or more of the determinations of step 101 may comprisedetermining the cardinality of the collection of linear combinations oftransmission and/or reception beams based on properties of a compressionmatrix representing the collection of linear combinations oftransmission beams and the collection of linear combinations ofreception beams.

At least one of the linear combinations of transmission beams may be alinear combination of at least two of the transmission beams of the setof the available transmission beams. Thus, the linear combination is notan identity function. Similarly, at least one of the linear combinationsof reception beams may be a linear combination of at least two of thereception beams of the set of the available reception beams.

In typical embodiments, each of the linear combinations of transmissionreception beams is a unique linear combination.

Also typically, each of the linear combinations oftransmission/reception beams is a linear combination of all of the beamsof the corresponding set.

The collection of linear combinations of transmission/reception beamsmay, for example, be defined by an approximately optimal Grassmanniancoding matrix. Thus, each of the collections of linear combinations oftransmission/reception beams may be defined by an N×K matrix withcolumns equal to K vectors from a complex Grassmannian packing problemin N dimensions; each column corresponding to an approximately optimalGrassmannian frame.

According to some embodiments, the collection of linear combinations oftransmission beams, representable by a matrix B_(TX), and the collectionof linear combinations of reception beams, representable by a matrixB_(RX), are determined such that is a substantially block diagonalmatrix, wherein A=B_(TX)⊗B_(RX) and ⊗ represents the Kronecker product.

Generally, any other suitable coding matrices may be used to define thecollections of linear combinations.

In step 101 a of the method 100, an indication of the collection oflinear combinations of reception beams is provided by the transmitterapparatus and, in step 151 of the method 150, the indication of thecollection of linear combinations of reception beams is acquired by thereceiver apparatus. The transferring of the indication of the collectionof linear combinations of reception beams between transmitter apparatusand receiver apparatus is represented by signaling 191 in FIG. 1C.

In step 102 of the method 100, each of the linear combinations oftransmission beams of the collection of linear combinations oftransmission beams is transmitted for beam selection measurements by thereceiver apparatus.

In typical embodiments, each of the linear combinations of transmissionbeams of the collection of linear combinations of transmission beams istransmitted in a respective transmission time resource, the respectivetime resources being different (from each other), i.e., one linearcombination of beams is transmitted at a time.

Alternatively, each of the linear combinations of transmission beams ofthe collection of linear combinations of transmission beams may betransmitted in a respective transmission frequency resource, therespective frequency resources being different (from each other), i.e.,one linear combination of beams is transmitted per frequency resource.

Yet alternatively, each of the linear combinations of transmission beamsof the collection of linear combinations of transmission beams may betransmitted in a respective transmission time-frequency resource, therespective time-frequency resources being different (from each other),i.e., one linear combination of beams is transmitted per time-frequencyresource. Thereby, several linear combinations of beams may betransmitted per time resource and/or several linear combinations ofbeams may be transmitted per frequency resource.

Transmission in respective time and/or frequency resources may beparticularly suitable when the beam structure of the channel does notchange significantly across the resources used (time, frequency, orboth).

In step 152 of the method 150, a number of measurement signals for beamselection measurements are received from the transmitter apparatus. Thenumber of measurement signals correspond to the collection of linearcombinations of transmission beams of the set of available transmissionbeams (e.g., the transmitted linear combinations as effected by thechannel). The reception of step 152 is performed using each of thelinear combinations of reception beams of the collection of linearcombinations of reception beams.

The transmission of the linear combinations of transmission beams of thecollection of linear combinations of transmission beams and thereception of the measurement signals corresponding to that collection isrepresented by signaling 192 in FIG. 1C.

Beam selection measurements are performed, in step 153 of the method150, on the number of measurement signals for selection of thetransmission beam from the plurality of available transmission beams andfor selection of the reception beam from the plurality of availablereception beams (e.g., for selection of a transmission-reception beampair). Such measurements may be according to any suitable approach.

For example, performing beam selection measurements may comprisedetermining a quality metric (e.g., signal strength, SNR, etc.) for eachcombination of a transmission beam of the set of available transmissionbeams and a reception beam of the set of available reception beams basedon the beam selection measurements (e.g., for eachtransmission-reception beam pair) based on the beam selectionmeasurements.

Alternatively or additionally, performing beam selection measurementsmay comprise subjecting the number of received measurement signals tomatched filtering, or minimum mean square error (MMSE) processing, ormaximum likelihood (ML) detection processing, based on the collection oflinear combinations of transmission beams and the collection of linearcombinations of reception beam.

Step 153 may also comprise selecting a reception beam from the pluralityof available reception beams. The selection may comprise selecting thereception beam of the best transmission-reception beam pair.

Optionally, a transmission beam selection measurement report istransmitted by the receiver apparatus, in step 154 of the method 150,for selection of the transmission beam from the plurality of availabletransmission beams. The transmission beam selection measurement reportmay be received by the transmitter apparatus, in step 104 of the method100.

The transmission beam selection measurement report may be indicative ofat least part of the selection measurement results (e.g. the qualitymetric) of the transmission beam of the best transmission-reception beampair. Alternatively or additionally, the transmission beam selectionmeasurement report may be indicative of a preferred transmission beam,or beams, determined by the receiver apparatus based on the selectionmeasurement results (e.g., by indicating an index of each preferredtransmission beam).

The transmission beam selection measurement report is represented bysignaling 194 in FIG. 1C.

In optional step 105, the transmitter apparatus selects the transmissionbeam (to be used for transmission to the receiver apparatus) from theplurality of available transmission beams in accordance with thereceived transmission beam selection measurement report. The selectionmay be performed using any suitable approach. For example, the selectionmay be based on selection measurement results according to someembodiments. In another example, the selection merely comprisesaccepting the preferred transmission beam indicated in the transmissionbeam selection measurement report.

Once selected, the transmission beam is used, in optional step 106 ofthe method 100, to transmit signals to the receiving apparatus, whichsignals are received by the receiving apparatus using the selectedreception beam, in optional step 156 of the method 150.

The transmission and reception of signals using the selectedtransmission/reception beams is represented by signaling 196 in FIG. 1C.

FIG. 2A schematically illustrates an example transmitter apparatus 210according to some embodiments. The transmitter apparatus is configuredto transmit signals to a receiver apparatus using a transmission beamselected from a plurality of available transmission beams. The receiverapparatus is configured to receive the signals using a reception beamselected from a plurality of available reception beams. A set of theavailable transmission beams and a set of the available reception beamsare for beam selection measurements by the receiver apparatus.

For example, the transmitter apparatus may be configured to perform (orcause performance of) one or more of the steps described in connectionwith the method 100 of FIG. 1A. The transmitter apparatus of FIG. 2A maybe comprised in a network node and/or a wireless communication device,for example. The apparatus comprises controlling circuitry (CNTR; e.g. acontroller or a controlling module) 200.

The controlling circuitry is configured to cause determination of acollection of linear combinations of transmission beams of the set ofthe available transmission beams and determination of a collection oflinear combinations of reception beams of the set of available receptionbeams (compare with step 101 of FIG. 1A). To this end, the controllingcircuitry may comprise, or be otherwise associated with (e.g., beoperably connectable, or connected, to), determination circuitry (DET;e.g., a determiner or a determination module) 201. The determinationcircuitry may be configured to determine the collection of linearcombinations of transmission beams of the set of the availabletransmission beams and the collection of linear combinations ofreception beams of the set of available reception beams.

The controlling circuitry may also be configured to cause provision ofan indication of the collection of linear combinations of receptionbeams to the receiver apparatus (compare with step 101 a of FIG. 1A). Tothis end, the controlling circuitry may comprise, or be otherwiseassociated with (e.g., be operably connectable, or connected, to),provision circuitry (e.g., a provider or a provision module). In FIG.2A, the provision circuitry is considered as comprised in thetransceiving circuitry (TX/TR) 230. The provision circuitry may beconfigured to provide the indication of the collection of linearcombinations of reception beams to the receiver apparatus.

The controlling circuitry may also be configured to cause transmissionof each of the linear combinations of transmission beams of thecollection of linear combinations of transmission beams for beamselection measurements by the receiver apparatus (compare with step 102of FIG. 1A). To this end, the controlling circuitry may comprise, or beotherwise associated with (e.g., be operably connectable, or connected,to), transmission circuitry (e.g., a transmitter or a transmissionmodule). In FIG. 2A, the transmission circuitry is considered ascomprised in the transceiving circuitry (TX/TR) 230. The transmissioncircuitry may be configured to transmit each of the linear combinationsof transmission beams of the collection of linear combinations oftransmission beams for beam selection measurements by the receiverapparatus.

The controlling circuitry may also be configured to cause reception of atransmission beam selection measurement report from the receiverapparatus (compare with step 104 of FIG. 1A), To this end, thecontrolling circuitry may comprise, or be otherwise associated with(e.g., be operably connectable, or connected, to), reception circuitry(e.g., a receiver or a reception module). In FIG. 2A, the receptioncircuitry is considered as comprised in the transceiving circuitry(TX/TR) 230. The reception circuitry may be configured to receive thetransmission beam selection measurement report from the receiverapparatus.

The controlling circuitry may also be configured to cause selection ofthe transmission beam from the plurality of available transmission beamsin accordance with the received transmission beam selection measurementreport (compare with step 105 of FIG. 1A). To this end, the controllingcircuitry may comprise, or be otherwise associated with (e.g., beoperably connectable, or connected, to), selection circuitry (SEL; e.g.,a selector or a selection module) 202. The selection circuitry may beconfigured to select the transmission beam from the plurality ofavailable transmission beams in accordance with the receivedtransmission beam selection measurement report.

The controlling circuitry may also be configured to cause transmissionof signals using the selected transmission beam (compare with step 106of FIG. 1A). To this end, the controlling circuitry may comprise, or beotherwise associated with (e.g., be operably connectable, or connected,to), transmission circuitry (e.g., a transmitter or a transmissionmodule). In FIG. 2A, the transmission circuitry is considered ascomprised in the transceiving circuitry (TX/TR) 230. The transmissioncircuitry may be configured to transmit signals using the selectedtransmission beam.

FIG. 2B schematically illustrates an example transmitter apparatus 250according to some embodiments. The transmitter apparatus is configuredto transmit signals to a receiver apparatus using a transmission beamselected from a plurality of available transmission beams. The receiverapparatus is configured to receive the signals using a reception beamselected from a plurality of available reception beams. A set of theavailable transmission beams and a set of the available reception beamsare for beam selection measurements by the receiver apparatus.

For example, the transmitter apparatus may be configured to perform (orcause performance of) one or more of the steps described in connectionwith the method 100 of FIG. 1A. The transmitter apparatus of FIG. 2B maybe comprised in a network node and/or a wireless communication device,for example.

The apparatus comprises a determiner (DET, e.g., a determination unit ordetermination module) 251 configured to determine a collection of linearcombinations of transmission beams of the set of the availabletransmission beams and a collection of linear combinations of receptionbeams of the set of available reception beams (compare with step 101 ofFIG. 1A).

The apparatus may also comprise a provider (PROV) 252 configured toprovide an indication of the collection of linear combinations ofreception beams to the receiver apparatus (compare with step 101 a ofFIG. 1A).

The apparatus also comprises a transmitter (TX 1) 253 configured totransmit each of the linear combinations of transmission beams of thecollection of linear combinations of transmission beams for beamselection measurements by the receiver apparatus (compare with step 102of FIG. 1A).

The apparatus may also comprise a receiver (RX) 255 configured toreceive a transmission beam selection measurement report from thereceiver apparatus (compare with step 104 of FIG. 1A).

The apparatus may also comprise a selector (SEL, e.g., a selection unitor selection module) 256 configured to select the transmission beam fromthe plurality of available transmission beams in accordance with thereceived transmission beam selection measurement report (compare withstep 105 of FIG. 1A).

The apparatus may also comprises a transmitter (TX 2) 257—which may bethe same as the transmitter 253—configured to transmit signals using theselected transmission beam (compare with step 106 of FIG. 1A).

FIG. 3A schematically illustrates an example receiver apparatus 310according to some embodiments. The receiver apparatus is configured toreceive, from a transmitter apparatus, signals using a reception beamselected from a plurality of available reception beams. The transmitterapparatus is configured to transmit the signals to the receiverapparatus using a transmission beam selected from a plurality ofavailable transmission beams. A set of the available transmission beamsand a set of the available reception beams are for beam selectionmeasurements by the receiver apparatus.

For example, the receiver apparatus may be configured to perform (orcause performance of) one or more of the steps described in connectionwith the method 150 of FIG. 1B. The transmitter apparatus of FIG. 3A maybe comprised in a network node and/or a wireless communication device,for example. The apparatus comprises controlling circuitry (CNTR; e.g. acontroller or a controlling module) 300.

The controlling circuitry may be configured to cause acquisition, fromthe transmitter apparatus, of an indication of a collection of linearcombinations of reception beams of the set of the available receptionbeams (compare with step 151 of FIG. 1B). To this end, the controllingcircuitry may comprise, or be otherwise associated with (e.g., beoperably connectable, or connected, to), acquisition circuitry (e.g., anacquirer or an acquisition module). In FIG. 3A, the acquisitioncircuitry is considered as comprised in the transceiving circuitry(TX/TR) 330. The acquisition circuitry may be configured to acquire,from the transmitter apparatus, an indication of a collection of linearcombinations of reception beams of the set of the available receptionbeams.

The controlling circuitry is also configured to cause reception, usingeach of the linear combinations of reception beams of the collection oflinear combinations of reception beams, of a number of measurementsignals for beam selection measurements from the transmitter apparatus,wherein the number of measurement signals correspond to a collection oflinear combinations of transmission beams of the set of availabletransmission beams (compare with step 152 of FIG. 1B), To this end, thecontrolling circuitry may comprise, or be otherwise associated with(e.g., be operably connectable, or connected, to), reception circuitry(e.g., a receiver or a reception module). In FIG. 3A, the receptioncircuitry is considered as comprised in the transceiving circuitry(TX/TR) 330. The reception circuitry may be configured to receive themeasurement signals for beam selection measurements from the transmitterapparatus.

The controlling circuitry is also configured to cause performance ofbeam selection measurements on the measurement signals (compare withstep 153 of FIG. 1B). To this end, the controlling circuitry maycomprise, or be otherwise associated with (e.g., be operablyconnectable, or connected, to), measuring circuitry (MEAS e.g., ameasurer or a measurement module) 301. The measuring circuitry may beconfigured to perform the beam selection measurements.

The controlling circuitry may also be configured to cause selection of areception beam from the plurality of available reception beams. To thisend, the controlling circuitry may comprise, or be otherwise associatedwith (e.g., be operably connectable, or connected, to), selectioncircuitry (SEL e.g., a selector or a selection module) 302. Theselection circuitry may be configured to select the reception beam fromthe plurality of available reception beams.

The controlling circuitry may also be configured to cause transmissionof a transmission beam selection measurement report to the transmitterapparatus for selection of the transmission beam from the plurality ofavailable transmission beams (compare with step 154 of FIG. 1B). To thisend, the controlling circuitry may comprise, or be otherwise associatedwith (e.g., be operably connectable, or connected, to), transmissioncircuitry (e.g., a transmitter or a transmission module). In FIG. 3A,the transmission circuitry is considered as comprised in thetransceiving circuitry (TX/TR) 330. The transmission circuitry may beconfigured to transmit the transmission beam selection measurementreport.

The controlling circuitry may also be configured to cause reception ofsignals using the selected reception beam (compare with step 156 of FIG.1B). To this end, the controlling circuitry may comprise, or beotherwise associated with (e.g., be operably connectable, or connected,to), reception circuitry (e.g., a receiver or a reception module). InFIG. 3A, the reception circuitry is considered as comprised in thetransceiving circuitry (TX/TR) 330. The reception circuitry may beconfigured to receive signals using the selected reception beam.

FIG. 3B schematically illustrates an example receiver apparatus 350according to some embodiments. The receiver apparatus is configured toreceive, from a transmitter apparatus, signals using a reception beamselected from a plurality of available reception beams. The transmitterapparatus is configured to transmit the signals to the receiverapparatus using a transmission beam selected from a plurality ofavailable transmission beams. A set of the available transmission beamsand a set of the available reception beams are for beam selectionmeasurements by the receiver apparatus.

For example, the receiver apparatus may be configured to perform (orcause performance of) one or more of the steps described in connectionwith the method 150 of FIG. 1B. The transmitter apparatus of FIG. 3B maybe comprised in a network node and/or a wireless communication device,for example.

The apparatus comprises an acquirer (ACQ; e.g., an acquisition unit oracquisition module) 352 configured to acquire, from the transmitterapparatus, an indication of a collection of linear combinations ofreception beams of the set of the available reception beams (comparewith step 151 of FIG. 1B).

The apparatus may also comprise a receiver (RX 1) 353 configured toreceive, using each of the linear combinations of reception beams of thecollection of linear combinations of reception beams, a number ofmeasurement signals for beam selection measurements from the transmitterapparatus, wherein the number of measurement signals correspond to acollection of linear combinations of transmission beams of the set ofavailable transmission beams (compare with step 152 of FIG. 1B).

The apparatus also comprises a measurer (MEAS; e.g., a measurement unitor measurement module) 354 configured to perform beam selectionmeasurements on the measurement signals (compare with step 153 of FIG.1B).

The apparatus may also comprise a selector (SEL; e.g., a selection unitor selection module) 356 configured to select a reception beam from theplurality of available reception beams.

The apparatus may also comprise a transmitter (TX) 355 configured totransmit a transmission beam selection measurement report to thetransmitter apparatus for selection of the transmission beam from theplurality of available transmission beams (compare with step 154 of FIG.1B).

The apparatus may also comprise a receiver (RX 2) 357—which may be thesame as the receiver 353—configured to receive signals using theselected reception beam (compare with step 156 of FIG. 1B).

Thus, according to some embodiments, beam compression (also denotedherein as beam coding) for reducing overhead of beam training isprovided. The compression may be applicable at the transmitter apparatusand/or at the receiver apparatus.

Coding of the original beams (the beams of the set(s)) is formulatedsuch that the number of coded beams at the transmitter apparatus and/orat the receiver apparatus are (preferably significantly) less than thenumber of original beams. The coded beams correspond to the linearcombinations of beams. When the transmitter apparatus (e.g., a BS)transmits the coded transmission beams and the receiver apparatus (e.g.,a UE) receives using the coded reception beams, the total time for beamtraining becomes significantly lower than when the original set(s) ofbeams are used.

The receiver apparatus may (in typical approaches) perform a simpleoperation (matched filtering (corresponding to a maximum likelihoodsolution), MMSE processing, or similar) to estimate which pair of theoriginal beams is best, and the index of the preferred originaltransmission beam may be fed back to the transmitter apparatus.

Thus, some embodiments aim at reducing the overhead of the beam sweepingprocedure. This may be achieved using adapted BS and UE beam sweepingcodebooks (reduced in size compared to the original, conventional, beamsweeping codebooks), which comprise linear combinations of the beams asdefined in the original codebooks.

If the matrix F_(BS) denotes the beam sweeping codebook at the BS(wherein the columns of F_(BS) are transmission beams) and F_(UE)denotes the beam sweeping codebook at the UE (wherein the columns ofF_(UE) are reception beams) some embodiments may comprise—instead of theBS transmitting each beam (column) of F_(BS), one slot at a time, andthe UE listening on each beam (column) of F_(UE), one slot at atime—creating new sets of beams at the BS and/or at the UE.

The new sets of beams may be represented by the matrices G_(BS) andG_(UE), respectively, and may be defined by the following lineartransformations G_(BS)=F_(BS)B_(BS) ^(T), G_(UE)=F_(UE)B_(UE) ^(T),where (.)^(T) denotes matrix transpose. These new matrices (codebooks)may replace the original ones, F_(BS) and F_(UE), at least during thetraining phase for beam selection.

These beams represented by the G_(BS) and G_(UE) are coded beams(respective collections of linear combinations), and B_(BS) and B_(UE)act as a codes on the original sets of beams in F_(BS) and F_(UE),respectively. In each transmission resource (e.g., time and/orfrequency), a linear combination of the transmission beams in F_(BS) istransmitted, and received using a linear combination of the receptionbeams in F_(UE). If B_(BS) has no zero-valued elements, all transmissionbeams of F_(BS) are transmitted in each transmission resource.

If L_(BS) denotes the number of rows in B_(BS) and L_(UE) denotes thenumber of rows in B_(UE) (which equal the number of columns in G_(BS)and G_(UE), respectively), the number of transmission resources (e.g.,in time and/or frequency) needed for beam sweeping is L_(BS)L_(UE).

When B_(BS) and B_(UE) are constructed such that L_(BS)L_(UE) is(substantially) smaller than N_(BS)N_(UE)—where N_(BS) denotes thenumber of transmission beams (columns) in F_(BS) and N_(UE) denotes thenumber of reception beams (columns) in F_(UE)—beam sweeping becomes moreresource efficient.

Hence, a significant reduction of training overhead for beam sweepingmay be achieved according to some embodiments. Possibly, this approachentails an increase in error probability for detection of the bestcombination of transmission-reception beams. However, properconstruction of the coding matrices B_(BS) and B_(UE) can make thiserror probability small.

One possible approach for the construction of the coding matrices B_(BS)and B_(UE) is to let them be Grassmannian frames matrices; e.g.,selecting the columns in B_(BS) as vectors from a complex Grassmannianpacking problem in N_(BS) dimensions, and selecting the columns inB_(UE) as vectors from a complex Grassmannian packing problem in N_(UE)dimensions.

Furthermore, the detector at the reception apparatus may be very simple.For example, the detector may be implemented as a matched filter that ismatched to the coding matrices in some embodiments.

According to some embodiments, it is assumed that the BS is aware of thenumber of antennas at the UE and the beam codebook size at the UE. Suchinformation may, for example, be signaled by the UE to the BS at somesuitable point in time (e.g., in connection withassociation/registration). Then, for a codebook size of N_(BS) at BS andN_(UE) at UE, the BS may determine Grassmannian matrices for the BS andthe UE that result in a codebook of L_(BS) beams at BS and L_(UE) beamsat UE. The BS informs the UE about which matrix the UE should choose(provides an indication of the collection of linear combinations ofreception beams to the receiver apparatus). The BS may also inform theUE about which matrix is chosen at the BS. Then, the BS transmits thetransmission beams that result from compression with the BS Grassmannianmatrix and the UE projects the received signal onto the reception beamsthat result from compression with the UE Grassmannian matrix. The UEdetermines the indices of the best transmission-reception beam pair andfeeds back the index of the best transmission beam to the BS.

An example will now be provided to illustrate the general descriptionsof FIGS. 1A-C, 2A-B and 3A-B. In this example, it is assumed that the BShas M_(BS) antennas and the UE has M_(UE) antennas.

A BS codebook F_(BS)=[f_(BS,1), . . . , f_(BS,K)] and a UE codebookF_(UE)=[f_(UE,1), . . . , f_(UE,K)] are considered for beam sweeping.The columns of these matrices are the beams for beam selection training(the sets of beams in the wording above). As described above, thesebeams may be DFT beams, where each element has a constant magnitude.

A goal of the training procedure may, for example, be know which pair ofthe beams (one beam from the set f_(BS,1), . . . , f_(BS,K) and one beamfrom the set f_(UE,1), . . . , f_(UE,K)) provides highest received SNRat the UE; typically for the BS to know which beam in F_(BS) it shoulduse when transmitting to the UE and for the UE to know which beam inF_(UE) it should use when receiving data from the BS.

This may be achieved, for example, by determining (at the UE) which ofthe N_(BS)N_(UE) values |F_(UE) ^(H)(:,i)HF_(BS)(:,j)|, 1≤i≤N_(UE),1≤j≤N_(BS) is largest, where denotes the downlink (DL) channel matrixand (.)^(H) denotes Hermitian transpose. The value |F_(UE)^(H)(:,i)HF_(BS)(:,j)| represents the effective channel gain (which isproportional to the SNR) when using beam i and beam j at the UE and BS,respectively.

When the UE has determined the largest combination, say (i_(i),j_(i)),it may report the index j_(i) to the BS (in a selection measurementreport; e.g., in a subsequent feedback phase) and receive a subsequentdata transmission on the reception beam F_(UE)(i_(i),:). Hence, indexi_(i) does not necessarily need to be reported to the BS.

A straightforward way to determine the largest |F_(UE)^(H)(:,i)HF_(BS)(:,j)| is to let the BS transmit the beams in itscodebook F_(BS), one transmission beam at a time, and the UE to receivethe incoming BS beams on each of the beams in its codebook F_(UE), onereception beam at a time as mentioned above, which results inN_(BS)N_(UE) transmissions from the BS to the UE.

As mentioned above, an approach to reducing the usage of communicationresources comprises—instead of transmitting and receiving across theoriginal beam codebooks F_(BS) and F_(UE)—using linear combinations ofthe beams of the original beam codebooks. Such linear combinations maybe achieved by linear encoding (performed by the BS and/or the UE) andmay result in new beam codebooks:G _(BS) =F _(BS) B _(BS) ^(T)G _(UE) =F _(UE) B _(UE) ^(H).

The matrices B_(BS) ^(T) and B_(UE) ^(H) are linear encoding matricesthat can be designed as suitable. They transform the original beam setsF_(BS) and F_(UE) into the reduced beam sets G_(BS) and G_(UE) (thecollections of linear combinations of transmission/reception beams).

Design of the matrices BS_(BS) ^(T) and B_(UE) ^(H) entails design of amatrix A=B_(BS)⊗B_(UE) (where ⊗ stands for the matrix Kroeneckerproduct), and vice versa. As before, (.)^(T) denotes matrix transposeand (.)^(H) denotes Hermitian transpose, and this selection oftranspositions results in the particular expression for A as will beexemplified later herein. Other embodiments, may use G_(BS)=F_(BS)B_(BS)^(H) and G_(UE)=F_(UE)B_(UE) ^(T), G_(BS)=F_(BS)B_(BS) ^(H) andG_(UE)=F_(UE)B_(UE) ^(T), or G_(BS)=F_(BS)B_(BS) ^(T) andG_(UE)=F_(UE)B_(UE) ^(T); and result in other expressions for A.Preferably, A should be designed to be suitable for the detectionproblem as specified below.

Thus, G_(BS) and G_(UE) may be used as new beam codebooks; the BS maytransmit the columns from G_(BS) and the UE may receive on the columnsof G_(UE). If L_(BS) denotes the number of columns in G_(BS) and L_(UE)denotes the number of columns in G_(UE), the total training overheadwhen G_(BS) and G_(UE) are used for training will be L_(BS)L_(UE).

Since the new beams of each of G_(BS) and G_(UE) are linear combinationsof the original beams of each of F_(RS) and F_(UE), respectively, thenew beams carry information about the original beams. According to someembodiments, it may be beneficial to have as few columns in G_(BS) andG_(UE) as possible (or to find G_(BS) and G_(UE) such thatL_(BS)L_(UE)<<N_(BS)N_(UE); e.g., to minimize the product of the numberof columns in G_(BS) and G_(UE)). Preferably, this should be achievedwithout sacrificing too much in performance of the determination of thelargest |F_(UE) ^(H)(:,i)HF_(BS)*:,j)|.

The reduced codebooks G_(BS) and G_(UE) may be used only during thetraining phase, in order to learn the largest combination |F_(UE)^(H)(:,i)HF_(BS)(:,j)|. Then, they do not completely replace theoriginal beam codebooks F_(BS) and F_(UE), which may be used in thesubsequent data transmission. Alternatively, the reduced codebooksG_(BS) and G_(UE) may be used during the training phase and forsubsequent data transmission, or only for subsequent data transmission.

If y_(m,n)=G_(UE)(:, m)^(H)HG_(BS)(:, n)+n_(m,n), 1≤m≤L_(UE),1≤n≤L_(BS), denotes the received sample at the UE when the UE receiveson beam G_(UE)(:, m) and BS transmits beams G_(BS)(:, n), the resultingsystem model may be expressed asy=(B _(BS) ⊗B _(UE))c+n=Ac+n,

where y=[y_(1,1) y_(2,1) . . . y_(L) _(UE) _(-L) _(BS) ]^(T) denotes thereceived samples corresponding to all transmission-receiver beam pairsstacked in a column vector, n=[n_(1,1) n_(2,1) . . . n_(L) _(UE) _(-L)_(BS) ]^(T) denotes the corresponding additive white Gaussian noise(AWGN) samples n_(n,m) stacked in a column vector, H denotes thedownlink channel matrix (e.g., for a MIMO channel; a MIMO channel on acertain subcarrier in case of an OFDM system), and c=vec(F_(UE)^(H)HF_(BS)).

The notation vec(F_(UE) ^(H)HF_(BS)) may be understood as the columns ofF_(UE) ^(H)HF_(BS) stacked on top of each other. Thus, if A is an N×Mmatrix where the i^(th) column is denoted a_(i), then vec(A) is an MN×1vector; vec(A)=[a_(i) ^(T) . . . a_(M) ^(T)]^(T). Using this modelexpression, the detection problem (determining the largest |F_(UE)^(T)(:, i)HF_(BS)(:, j)|) translates to finding the index of the elementin c with highest magnitude. Therefrom, the preferred pair oftransmission-reception beams can be determined.

At first glance, it might appear that the detection problem is illconditioned since A is a L_(BS)L_(UE)×N_(BS)N_(UE) matrix that has morecolumns than rows. However, under certain statistical assumptions for cand a certain structure of A (both of which will be exemplified below),a simple matched filter (matched to the matrix A) followed by locatingthe element with largest magnitude performs very well.

Thus, one possible decoder for the index k of the element in c withlargest magnitude is obtained as {circumflex over (k)}=arg

(A^(H)y)_(k)|, where (A^(H)y)_(k) is the k:th element in the vectorA^(H)y.

From the index {circumflex over (k)}, the index of the preferredreception beam can be determined as mod({circumflex over (k)}−1,M_(UE))+1, where mod(a, b) is the rest when a is divided by b, and theindex of the preferred transmission beam can be determined as┌{circumflex over (k)}/M_(UE)┐, where ┌.┐ is the ceiling operator.

It is possible to compress the original codebooks into smaller ones aselaborated on above, while still obtaining small error probability inthe detection (determination) of the “best” combination of beams fromthe original codebooks (e.g., the transmission-reception beam pairhaving the largest value of |F_(UE) ^(H)(:,i)HF_(BS)(:,j)|) with thesimple matched filter receiver. As mentioned above, this is possibleunder certain statistical assumptions for c and a certain structure ofA.

An example of such a certain structure of A is when A_(BS)⊗B_(UE) hasunitary-like properties, and an example of such certain statisticalassumptions for c is when the vector c is sparse. Examples ofunitary-like properties include a diagonal dominant structure and/or alow spread of non-zero eigenvalues.

A matrix with low spread of non-zero eigenvalues may, for example, bedefined as a matrix where the ratio between the magnitude of thenon-zero eigenvalue having the largest magnitude and the magnitude ofthe non-zero eigenvalue having the smallest magnitude is less than acertain percentage (e.g. 20%, 10%, 5%, 1%, 0.1%, 0.01%) of the number ofnon-zero eigenvalues.

A sparse vector may, for example be defined as a vector where more thana threshold, e.g., a certain percentage (e.g., 80%, 90%, 95% or 99%),but less than all, of the elements equal zero.

A diagonal dominant structure of a matrix may, for example be defined asa matrix where all elements, which are offset to the diagonal with morethan a threshold, e.g., a certain percentage (e.g., 1%, 2%, 3%, 5%, 10%,or 20%) of the number of rows (or columns) of the matrix, equal zero (orhas a magnitude that is less than a threshold, e.g., a certainpercentage (e.g., 1%, 2%, 3%, 5%, 10%, or 20%) of the largest magnitudeof the matrix elements).

Alternatively, a diagonally dominant matrix may be defined as a matrixwhere the ratio between the sum of the magnitudes of the diagonalelements and the sum of the magnitudes of the non-diagonal elements issmaller than a threshold value (e.g. 1, 0.5, 0.1, 0.01); regardless ofwhether or not there are zero-valued off-diagonal elements.

One way of achieving that A has unitary-like properties is to let thecoding matrices B_(BS) and B_(UE) be Grassmannian frames/matrices. Sucha choice results in that the Gram of A (i.e., A^(H)A) has propertiesthat—for detection purposes—resemble the properties of an identitymatrix. Typically, less compression leads to better resemblance.Examples of such properties include that A^(H)A has a diagonal dominantstructure, and that the spread between the non-zero eigenvalues ofA^(H)A is low.

Sparsity of the vector c depends on the properties of the downlinkchannel matrix H. Sparsity exists, e.g., in relation to mmW (millimetrewavelength) channels. Sparsity of the vector c may be beneficial for thedetection since the non-zero elements in c (other than the element withlargest magnitude) act as interference for the detector, Thus, sparsityof c entails low interference for the detection, which typically isimportant for good detection performance. Sparsity of c may also entailthat a structure of A having more columns than rows does not result inan ill-posed detection problem. This is because, during detection, onlya few columns of A—those corresponding to a non-zero elements in c—areactivated at a time when c is sparse.

Under these assumptions, a matched filter detector performs almost asgood as a detector based on maximum likelihood (ML) decoding.

Generally, when an arrangement is referred to herein, it is to beunderstood as a physical product; e.g., an apparatus. The physicalproduct may comprise one or more parts, such as controlling circuitry inthe form of one or more controllers, one or more processors, or thelike.

The described embodiments and their equivalents may be realized insoftware or hardware or a combination thereof. The embodiments may beperformed by general purpose circuitry. Examples of general purposecircuitry include digital signal processors (DSP), central processingunits (CPU), co-processor units, field programmable gate arrays (FPGA)and other programmable hardware. Alternatively or additionally, theembodiments may be performed by specialized circuitry, such asapplication specific integrated circuits (ASIC). The general purposecircuitry and/or the specialized circuitry may, for example, beassociated with or comprised in an apparatus such as a wirelesscommunication device or a network node.

Embodiments may appear within an electronic apparatus (such as awireless communication device or a network node) comprisingarrangements, circuitry, and/or logic according to any of theembodiments described herein. Alternatively or additionally, anelectronic apparatus (such as a wireless communication device or anetwork node) may be configured to perform methods according to any ofthe embodiments described herein.

According to some embodiments, a computer program product comprises acomputer readable medium such as, for example a universal serial bus(USB) memory, a plug-in card, an embedded drive or a read only memory(ROM). FIG. 4 illustrates an example computer readable medium in theform of a compact disc (CD) ROM 400. The computer readable medium hasstored thereon a computer program comprising program instructions. Thecomputer program is loadable into a data processor (PROC) 420, whichmay, for example, be comprised in a wireless communication device or anetwork node 410. When loaded into the data processing unit, thecomputer program may be stored in a memory (MEM) 430 associated with orcomprised in the data-processing unit. According to some embodiments,the computer program may, when loaded into and run by the dataprocessing unit, cause execution of method steps according to, forexample, any of the methods illustrated in FIGS. 1A and 1B, or otherwisedescribed herein.

FIGS. 5A and 5B are simulation plots illustrating example resultsobtainable by application of some beam sweeping compression embodiments.In these simulations, it was assumed that the downlink M_(UE)×M_(BS)MIMO channel H represents a narrowband MIMO channel (e.g. a MIMO channelon an OFDM subcarrier), which can be expressed as

${H = {\sum\limits_{i = 1}^{L}{a_{1}{e_{UE}\left( \theta_{i} \right)}{e_{BS}\left( \phi_{i} \right)}^{T}}}},$

where a_(i) are complex Gaussian scalars with unit variance, L denotesthe number of simultaneously received reflections, e_(UE)(θ)=[1e^(iπ sin(θ)) . . . e^(iπ(M) ^(EU) ^(-1)sin(θ))]^(T), and e_(BS)(ϕ)=[1e^(iπ sin(ϕ)) . . . e^(iπ(M) ^(BS) ^(-1)sin(ϕ))]^(T). In a mmW scenario,L is small (typically L≤10). In an outdoor scenario with dominantline-of-sight (LOS) and ground reflection, L=2.

The simulation results illustrated in FIGS. 5A and 5B represent twodifferent types of codebook constructions for F_(BS) and F_(UE). In thefirst construction (FIG. 5a ), the beam vectors in F_(BS) and F_(UE) areuniformly spread analog beams in the azimuth direction; which is thetypical codebook used for a mmW channel. The second construction (FIG.5B) is a more narrow codebook, where the beams in F_(BS) and F_(UE) areconcentrated around a certain direction; which is typical for beamtracking where the codebooks are adjusted to be concentrated around thelast found best beam combination. The second construction results in aless sparse vector c than the first construction, which will entailworse detection performance; especially when the compression is aslarge.

FIG. 5A shows the beam selection performance (loss in dB with regard tooptimal beam—20 log(|F_(UE) ^(H)(:,i*)HF_(BS)(:,j)|)−20 log(|F_(UE)^(H)(:,î)HF_(BS)(:,ĵ)|), where î and ĵ are the estimates of the indexesof the optimal beam pair i* and j*—versus SNR in dB) in the case of auniformly spread codebook, where L=4 paths are assumed in the MIMOchannel, the BS has 64 antennas (and as many beams in the originalcodebook) and the UE has 16 antennas (and as many beams in the originalcodebook).

The curve 504 (uppermost at high SNR) represents the case when there isno compression at either of the BS and UE, i.e., the BS transmits eachbeam From F_(BS) separately, and the UE listens on each beam from F_(UE)separately. It is expected that this curve will in general have the bestperformance (it saturates at roughly 0 dB loss compared to the optimalbeam, i.e., it manages to report the optimal beam at high enough SNRs).This case requires 16×64=1024 transmission resources.

The curves 501, 502, 503 represent different levels of compression. Thecurve 501 represent using 8 linear combinations of beams at the UE and40 linear combinations of beams at the BS. The curve 502 represent using10 linear combinations of beams at the UE and 32 linear combinations ofbeams at the BS. The curve 503 represent using 10 linear combinations ofbeams at the UE and 40 linear combinations of beams at the BS.

As seen from FIG. 5A, a compression of the BS codebook to 32 beams andof the UE codebook to 10 beams (refer to curve 502) results in only amarginal loss (saturating at a loss of 0.37 dB) compared to the casewith no compression; across all ranges of SNR, This case requires10×32=320 transmission resources; a saving of

$\frac{1024 - 320}{1024} \approx {69\%}$compared to the case with no compression.

Another interesting observation from FIG. 5A is that the curve 501 hassignificantly worse performance than the curve 502, although theyrequire the same number of transmission resources. This indicates thatit may be important how the compression is distributed between thetransmitter apparatus and the receiver apparatus. Typically, if thecompression is too large at any side, the performance will start todegrade.

FIG. 5B shows the beam selection performance (loss in dB with regard tooptimal beam versus SNR in dB) in the case where the codebooks at the BSand the UE are adapted to the strongest path in the channel; a beamtracking scenario. As for FIG. 5A, L=4 paths are assumed in the MIMOchannel, the BS has 64 antennas (and as many beams in the originalcodebook) and the UE has 16 antennas (and as many beams in the originalcodebook).

The strongest path is the term in

$H = {\sum\limits_{i = 1}^{L}{a_{1}{e_{UE}\left( \theta_{i} \right)}{e_{BS}\left( \phi_{i} \right)}^{T}}}$with largest value of |a_(i)|. If θ is the UE angle of the strongestpath and ϕ is the BS angle of the strongest path in, then the UEcodebook consists of beams with angles uniformly spread in

$\left\lbrack {{\theta - \frac{\pi}{4}},{\theta + \frac{\pi}{4}}} \right\rbrack$and the BS codebook consists of beams with angles uniformly spread in

$\left\lbrack {{\phi - \frac{\pi}{4}},{\phi + \frac{\pi}{4}}} \right\rbrack.$

The curve 511 (uppermost) represents the case when there is nocompression at either of the BS and UE, i.e., the BS transmits each beamfrom F_(BS) separately, and the UE listens on each beam from F_(UE)separately. It is expected that this curve will in general have the bestperformance. This case requires 16×64=1024 transmission resources.

The curves 512, 513, 514, 515 represent different levels of compression.The curve 512 represent using 10 linear combinations of beams at the UEand 48 linear combinations of beams at the BS. The curve 513 representusing 10 linear combinations of beams at the UE and 40 linearcombinations of beams at the BS. The curve 514 represent using 10 linearcombinations of beams at the UE and 32 linear combinations of beams atthe BS. The curve 515 represent using 8 linear combinations of beams atthe UE and 40 linear combinations of beams at the BS.

Comparing FIG. 5B with FIG. 5A, it may be seen that the compression nowcauses a more prominent loss compared to the approach with nocompression. The reason is that the vector c is not as sparse in FIG. 5Bas in FIG. 5A. Therefore, the performance of the matched filterestimation will suffer from strong interference. Hence, sparsity of cmay be important to not loose in detection performance for substantialcompression.

Nevertheless, the performance may still be acceptable. Reducing the beamsweeping overhead—the required number of transmission resources—withmore than 50% compared to no compression (going from 64×16=1024 forcurve 511 to 10×48=480 for curve 512) results in a loss of 0.6 dB.

Similarly to in FIG. 5A it may be noted in FIG. 5B that the curve 515has significantly worse performance than the curve 514, although theyrequire the same number of transmission resources, which indicates thatit may be important how the compression is distributed between thetransmitter apparatus and the receiver apparatus.

Since it may be important how the compression is distributed between thetransmitter apparatus and the receiver apparatus, joint determination ofthe collection of linear combinations of transmission beams and thecollection of linear combinations of reception beams may be beneficial.Various aspects of such joint determination will now be exemplified.

Of course, the approaches of joint determination may be restricted bywhat information is available. Furthermore, constrains (e.g.,complexity, delay, etc.) in the transmitter and/or receiverimplementation may provide conditions for the joint determination.

In a first example of joint determination, the determination is madesolely based on the structure of the matrix A=B_(BS)⊗B_(UE). Thisexample may be applicable, for example, when there is no availableinformation about the propagation channel. In this example, the diagonalelements of A^(H)A act as the desirable signal and the off-diagonalelements of A^(H)A act as interference. The signal-to-interference ratio(i.e., the sum of the energy of all diagonal elements divided by the sumof the energy of the all off-diagonal elements) may be used as adetermination metric, and B_(BS) and B_(UE) may be selected to maximizethis metric for a given amount of compression. For example, if there are10 candidate beams at the BS as well as at the UE (i.e., 100 beam paircandidates) and an overall compression factor of 50% is desired, thenpossible compression distributions include B_(BS) and B_(UE) having 7columns each, B_(BS) having 8 columns and B_(UE) having 6 columns, etc.Then, the compression distribution is chosen that entails the largestsignal-to-interference ratio as defined above.

In a second example of joint determination, knowledge is available(e.g., from channel estimations) regarding how many transmission andreception propagation paths are present in the downlink channel (i.e.,how sparse the channel is seen from the transmitter apparatus and fromthe receiver apparatus). Then, even if an overall compression factor of50% is desired and if there are 10 candidate beams at the BS as well asat the UE (i.e., 100 beam pair candidates), a compression distributionwhere B_(BS) and B_(UE) have 7 columns each would not perform well if,for example, 7 transmission paths and 2 reception paths are present. Inthis example, a suitable determination metric may be similarity betweentransmitter side and receiver side of respective ratio of the number ofbeams and the number of paths present. When 7 transmission paths and 2reception paths are present a good compression distribution may beB_(BS) having 10 columns (i.e., no compression) and B_(UE) having 5columns since then the ratios (10/7≈1.4 and 5/2=2.5) become as similaras possible. If there were more beams available at the BS, a bettercompression distribution may be B_(BS) having 12 columns (i.e., nocompression) and B_(UE) having 4 columns since then the ratios (12/7≈1.7and 4/2=2) become even more similar.

One way of acquiring knowledge of the number of paths present may be viaapplication of subspace estimation via singular value decomposition(SVD). In such an approach, a starting point may be knowledge regardingall the received signals from the latest beam sweeping procedure and/orthe received signals from online channel measurements using referencesignals. Using an assumption that the current number of paths is thesame, or very similar, to the number of paths present at the time of thelatest beam sweep and/or channel measurements, the spatial covariancematrix can be estimated for the BS and for the UE. The number ofdominant singular values, after singular value decomposition, of eachthese covariance matrices may constitute an estimate of the number ofpresent paths at the BS and at the UE, respectively.

In a third example, a hybrid between the first example (matrixsignal-to-interference ratio detection) and the second example(similarity of beam-path ratios) is applied. For example, if the firstexample indicates that B_(BS) and B_(UE) should have 7 columns each andthe second example indicates that B_(BS) should have 10 columns andB_(UE) should have 5 columns, an intermediary solution where B_(BS) has8 columns and B_(UE) has 6 columns may be applicable according to thisexample.

With reference to FIG. 6, in accordance with an embodiment, acommunication system includes telecommunication network QQ410, such as a3GPP-type cellular network, which comprises access network QQ411, suchas a radio access network, and core network QQ414. Access network QQ411comprises a plurality of base stations QQ412 a, QQ412 b, QQ412 c, suchas NBs, eNBs, gNBs or other types of wireless access points, eachdefining a corresponding coverage area QQ413 a, QQ413 b, QQ413 c. Eachbase station QQ412 a, QQ412 b, QQ412 c is connectable to core networkQQ414 over a wired or wireless connection QQ415. A first UE QQ491located in coverage area QQ413 c is configured to wirelessly connect to,or be paged by, the corresponding base station QQ412 c, A second UEQQ492 in coverage area QQ413 a is wirelessly connectable to thecorresponding base station QQ412 a. While a plurality of UEs QQ491,QQ492 are illustrated in this example, the disclosed embodiments areequally applicable to a situation where a sole UE is in the coveragearea or where a sole UE is connecting to the corresponding base stationQQ412.

Telecommunication network QQ410 is itself connected to host computerQQ430, which may be embodied in the hardware and/or software of astandalone server, a cloud-implemented server, a distributed server oras processing resources in a server farm. Host computer QQ430 may beunder the ownership or control of a service provider, or may be operatedby the service provider or on behalf of the service provider,Connections QQ421 and QQ422 between telecommunication network QQ410 andhost computer QQ430 may extend directly from core network QQ414 to hostcomputer QQ430 or may go via an optional intermediate network QQ420.Intermediate network QQ420 may be one of, or a combination of more thanone of, a public, private or hosted network; intermediate network QQ420,if any, may be a backbone network or the Internet; in particular,intermediate network QQ420 may comprise two or more sub-networks (notshown).

The communication system of FIG. 6 as a whole enables connectivitybetween the connected UEs QQ491, QQ492 and host computer QQ430. Theconnectivity may be described as an over-the-top (OTT) connection QQ450.Host computer QQ430 and the connected UEs QQ491, QQ492 are configured tocommunicate data and/or signaling via OTT connection QQ450, using accessnetwork QQ411, core network QQ414, any intermediate network QQ420 andpossible further infrastructure (not shown) as intermediaries. OTTconnection QQ450 may be transparent in the sense that the participatingcommunication devices through which OTT connection QQ450 passes areunaware of routing of uplink and downlink communications. For example,base station QQ412 may not or need not be informed about the pastrouting of an incoming downlink communication with data originating fromhost computer QQ430 to be forwarded (e.g., handed over) to a connectedUE QQ491. Similarly, base station QQ412 need not be aware of the futurerouting of an outgoing uplink communication originating from the UEQQ491 towards the host computer QQ430.

Example implementations, in accordance with an embodiment, of the UE,base station and host computer discussed in the preceding paragraphswill now be described with reference to FIG. 7. In communication systemQQ500, host computer QQ510 comprises hardware QQ515 includingcommunication interface QQ516 configured to set up and maintain a wiredor wireless connection with an interface of a different communicationdevice of communication system QQ500. Host computer QQ510 furthercomprises processing circuitry QQ518, which may have storage and/orprocessing capabilities. In particular, processing circuitry QQ518 maycomprise one or more programmable processors, application-specificintegrated circuits, field programmable gate arrays or combinations ofthese (not shown) adapted to execute instructions. Host computer QQ510further comprises software QQ511, which is stored in or accessible byhost computer QQ510 and executable by processing circuitry QQ518.Software QQ511 includes host application QQ512. Host application QQ512may be operable to provide a service to a remote user, such as UE QQ530connecting via OTT connection QQ550 terminating at UE QQ530 and hostcomputer QQ510. In providing the service to the remote user, hostapplication QQ512 may provide user data which is transmitted using OTTconnection QQ550.

Communication system QQ500 further includes base station QQ520 providedin a telecommunication system and comprising hardware QQ525 enabling itto communicate with host computer QQ510 and with UE QQ530. HardwareQQ525 may include communication interface QQ526 for setting up andmaintaining a wired or wireless connection with an interface of adifferent communication device of communication system QQ500, as well asradio interface QQ527 for setting up and maintaining at least wirelessconnection QQ570 with UE QQ530 located in a coverage area (not shown inFIG. 7) served by base station QQ520. Communication interface QQ526 maybe configured to facilitate connection QQ560 to host computer QQ510.Connection QQ560 may be direct or it may pass through a core network(not shown in FIG. 7) of the telecommunication system and/or through oneor more intermediate networks outside the telecommunication system. Inthe embodiment shown, hardware QQ525 of base station QQ520 furtherincludes processing circuitry QQ528, which may comprise one or moreprogrammable processors, application-specific integrated circuits, fieldprogrammable gate arrays or combinations of these (not shown) adapted toexecute instructions. Base station QQ520 further has software QQ521stored internally or accessible via an external connection.

Communication system QQ500 further includes UE QQ530 already referredto. Its hardware QQ535 may include radio interface QQ537 configured toset up and maintain wireless connection QQ570 with a base stationserving a coverage area in which UE QQ530 is currently located. HardwareQQ535 of UE QQ530 further includes processing circuitry QQ538, which maycomprise one or more programmable processors, application-specificintegrated circuits, field programmable gate arrays or combinations ofthese (not shown) adapted to execute instructions. UE QQ530 furthercomprises software QQ531, which is stored in or accessible by UE QQ530and executable by processing circuitry QQ538. Software QQ531 includesclient application QQ532. Client application QQ532 may be operable toprovide a service to a human or non-human user via UE QQ530, with thesupport of host computer QQ510. In host computer QQ510, an executinghost application QQ512 may communicate with the executing clientapplication QQ532 via OTT connection QQ550 terminating at UE QQ530 andhost computer QQ510. In providing the service to the user, clientapplication QQ532 may receive request data from host application QQ512and provide user data in response to the request data. OTT connectionQQ550 may transfer both the request data and the user data. Clientapplication QQ532 may interact with the user to generate the user datathat it provides.

It is noted that host computer QQ510, base station QQ520 and UE QQ530illustrated in FIG. 7 may be similar or identical to host computerQQ430, one of base stations QQ412 a, QQ412 b, QQ412 c and one of UEsQQ491, QQ492 of FIG. 6, respectively. This is to say, the inner workingsof these entities may be as shown in FIG. 7 and independently, thesurrounding network topology may be that of FIG. 6.

In FIG. 7, OTT connection QQ550 has been drawn abstractly to illustratethe communication between host computer QQ510 and UE QQ530 via basestation QQ520, without explicit reference to any intermediary devicesand the precise routing of messages via these devices, Networkinfrastructure may determine the routing, which it may be configured tohide from UE QQ530 or from the service provider operating host computerQQ510, or both. While OTT connection QQ550 is active, the networkinfrastructure may further take decisions by which it dynamicallychanges the routing (e.g., on the basis of load balancing considerationor reconfiguration of the network).

Wireless connection QQ570 between UE QQ530 and base station QQ520 is inaccordance with the teachings of the embodiments described throughoutthis disclosure. One or more of the various embodiments improve theperformance of OTT services provided to UE QQ530 using OTT connectionQQ550, in which wireless connection QQ570 forms the last segment. Moreprecisely, the teachings of these embodiments may improve the signalingefficiency and thereby provide benefits such as improved capacity, forexample.

A measurement procedure may be provided for the purpose of monitoringdata rate, latency and other factors on which the one or moreembodiments improve. There may further be an optional networkfunctionality for reconfiguring OTT connection QQ550 between hostcomputer QQ510 and UE QQ530, in response to variations in themeasurement results. The measurement procedure and/or the networkfunctionality for reconfiguring OTT connection QQ550 may be implementedin software QQ511 and hardware QQ515 of host computer QQ510 or insoftware QQ531 and hardware QQ535 of UE QQ530, or both. In embodiments,sensors (not shown) may be deployed in or in association withcommunication devices through which OTT connection QQ550 passes; thesensors may participate in the measurement procedure by supplying valuesof the monitored quantities exemplified above, or supplying values ofother physical quantities from which software QQ511, QQ531 may computeor estimate the monitored quantities. The reconfiguring of OTTconnection QQ550 may include message format, retransmission settings,preferred routing etc.; the reconfiguring need not affect base stationQQ520, and it may be unknown or imperceptible to base station QQ520.Such procedures and functionalities may be known and practiced in theart. In certain embodiments, measurements may involve proprietary UEsignaling facilitating host computer QQ510's measurements of throughput,propagation times, latency and the like. The measurements may beimplemented in that software QQ511 and QQ531 causes messages to betransmitted, in particular empty or ‘dummy’ messages, using OTTconnection QQ550 while it monitors propagation times, errors etc.

FIG. 8 is a flowchart illustrating a method implemented in acommunication system, in accordance with one embodiment. Thecommunication system includes a host computer, a base station and a UEwhich may be those described with reference to FIGS. 6 and 7. Forsimplicity of the present disclosure, only drawing references to FIG. 8will be included in this section. In step QQ610, the host computerprovides user data. In substep QQ611 (which may be optional) of stepQQ610, the host computer provides the user data by executing a hostapplication. In step QQ620, the host computer initiates a transmissioncarrying the user data to the UE. In step QQ630 (which may be optional),the base station transmits to the UE the user data which was carried inthe transmission that the host computer initiated, in accordance withthe teachings of the embodiments described throughout this disclosure.In step QQ640 (which may also be optional), the UE executes a clientapplication associated with the host application executed by the hostcomputer.

FIG. 9 is a flowchart illustrating a method implemented in acommunication system, in accordance with one embodiment. Thecommunication system includes a host computer, a base station and a UEwhich may be those described with reference to FIGS. 6 and 7. Forsimplicity of the present disclosure, only drawing references to FIG. 9will be included in this section. In step QQ710 of the method, the hostcomputer provides user data. In an optional substep (not shown) the hostcomputer provides the user data by executing a host application. In stepQQ720, the host computer initiates a transmission carrying the user datato the UE. The transmission may pass via the base station, in accordancewith the teachings of the embodiments described throughout thisdisclosure. In step QQ730 (which may be optional), the UE receives theuser data carried in the transmission.

FIG. 10 is a flowchart illustrating a method implemented in acommunication system, in accordance with one embodiment. Thecommunication system includes a host computer, a base station and a UEwhich may be those described with reference to FIGS. 6 and 6. Forsimplicity of the present disclosure, only drawing references to FIG. 10will be included in this section. In step QQ810 (which may be optional),the UE receives input data provided by the host computer. Additionallyor alternatively, in step QQ820, the UE provides user data. In substepQQ821 (which may be optional) of step QQ820, the UE provides the userdata by executing a client application. In substep QQ811 (which may beoptional) of step QQ810, the UE executes a client application whichprovides the user data in reaction to the received input data providedby the host computer. In providing the user data, the executed clientapplication may further consider user input received from the user.Regardless of the specific manner in which the user data was provided,the UE initiates, in substep QQ830 (which may be optional), transmissionof the user data to the host computer. In step QQ840 of the method, thehost computer receives the user data transmitted from the UE, inaccordance with the teachings of the embodiments described throughoutthis disclosure.

FIG. 11 is a flowchart illustrating a method implemented in acommunication system, in accordance with one embodiment. Thecommunication system includes a host computer, a base station and a UEwhich may be those described with reference to FIGS. 6 and 7. Forsimplicity of the present disclosure, only drawing references to FIG. 11will be included in this section. In step QQ910 (which may be optional),in accordance with the teachings of the embodiments described throughoutthis disclosure, the base station receives user data from the UE. Instep QQ920 (which may be optional), the base station initiatestransmission of the received user data to the host computer. In stepQQ930 (which may be optional), the host computer receives the user datacarried in the transmission initiated by the base station.

SOME EXAMPLE EMBODIMENTS Group A Embodiments

-   A1. A method performed by a wireless device—transmitter    apparatus—for beam forming, wherein the transmitter apparatus is    configured to transmit signals to a receiver apparatus using a    transmission beam selected from a plurality of available    transmission beams, wherein the receiver apparatus is configured to    receive the signals using a reception beam selected from a plurality    of available reception beams, and wherein a set of the available    transmission beams and a set of the available reception beams are    for beam selection measurements by the receiver apparatus, the    method comprising:    -   determining a collection of linear combinations of transmission        beams of the set of the available transmission beams;    -   determining a collection of linear combinations of reception        beams of the set of available reception beams;    -   providing an indication of the collection of linear combinations        of reception beams to the receiver apparatus; and    -   transmitting each of the linear combinations of transmission        beams of the collection of linear combinations of transmission        beams for beam selection measurements by the receiver apparatus.-   A2. The method of any of the previous embodiments in Group A,    further comprising:    -   providing user data; and    -   forwarding the user data to a host computer via the transmission        to the base station.

Group B Embodiments

-   B1. A method performed by a base station—transmitter apparatus—for    beam forming, wherein the transmitter apparatus is configured to    transmit signals to a receiver apparatus using a transmission beam    selected from a plurality of available transmission beams, wherein    the receiver apparatus is configured to receive the signals using a    reception beam selected from a plurality of available reception    beams, and wherein a set of the available transmission beams and a    set of the available reception beams are for beam selection    measurements by the receiver apparatus, the method comprising:    -   determining a collection of linear combinations of transmission        beams of the set of the available transmission beams;    -   determining a collection of linear combinations of reception        beams of the set of available reception beams;    -   providing an indication of the collection of linear combinations        of reception beams to the receiver apparatus; and    -   transmitting each of the linear combinations of transmission        beams of the collection of linear combinations of transmission        beams for beam selection measurements by the receiver apparatus.-   B2. The method of any of the previous embodiments in Group B,    further comprising:    -   obtaining user data; and    -   forwarding the user data to a host computer or a wireless        device.

Group C Embodiments

-   C1. A wireless device for beamforming, the wireless device    comprising:    -   processing circuitry configured to perform any of the steps of        any of the Group A embodiments; and    -   power supply circuitry configured to supply power to the        wireless device.-   C2. A base station for beam forming, the base station comprising:    -   processing circuitry configured to perform any of the steps of        any of the Group B embodiments;    -   power supply circuitry configured to supply power to the base        station.-   C3. A user equipment (LE) for beam forming, the UE comprising:    -   an antenna configured to send and receive wireless signals;    -   radio front-end circuitry connected to the antenna and to        processing circuitry, and configured to condition signals        communicated between the antenna and the processing circuitry;    -   the processing circuitry being configured to perform any of the        steps of any of the Group A embodiments;    -   an input interface connected to the processing circuitry and        configured to allow input of information into the UE to be        processed by the processing circuitry;    -   an output interface connected to the processing circuitry and        configured to output information from the UE that has been        processed by the processing circuitry; and    -   a battery connected to the processing circuitry and configured        to supply power to the UE.

Group D Embodiments

-   D1. A communication system including a host computer comprising:    -   processing circuitry configured to provide user data; and    -   a communication interface configured to forward the user data to        a cellular network for transmission to a user equipment (UE),    -   wherein the cellular network comprises a base station having a        radio interface and processing circuitry, the base station's        processing circuitry configured to perform any of the steps        described for the Group B embodiments.-   D2. The communication system of embodiment D1 further including the    base station,-   D3. The communication system of any of embodiments D1 through D2,    further including the UE, wherein the UE is configured to    communicate with the base station.-   D4. The communication system of any of embodiments D1 through D3,    wherein:    -   the processing circuitry of the host computer is configured to        execute a host application, thereby providing the user data; and    -   the UE comprises processing circuitry configured to execute a        client application associated with the host application.-   D5. A method implemented in a communication system including a host    computer, a base station and a user equipment (UE), the method    comprising:    -   at the host computer, providing user data; and    -   at the host computer, initiating a transmission carrying the        user data to the UE via a cellular network comprising the base        station, wherein the base station performs any of the steps        described for the Group B embodiments.-   D6. The method of embodiment D5, further comprising, at the base    station, transmitting the user data.-   D7. The method of any of embodiments D5 through D6, wherein the user    data is provided at the host computer by executing a host    application, the method further comprising, at the UE, executing a    client application associated with the host application.-   D8. A user equipment (UE) configured to communicate with a base    station, the UE comprising a radio interface and processing    circuitry configured to perform the method of any of embodiments D5    through D7.-   D9. A communication system including a host computer comprising:    -   processing circuitry configured to provide user data; and    -   a communication interface configured to forward user data to a        cellular network for transmission to a user equipment (UE),    -   wherein the UE comprises a radio interface and processing        circuitry, the UE's components configured to perform any of the        steps described for the Group A embodiments.-   D10. The communication system of embodiment D9, wherein the cellular    network further includes a base station configured to communicate    with the UE.-   D11. The communication system of any of embodiments D9 through D10,    wherein:    -   the processing circuitry of the host computer is configured to        execute a host application, thereby providing the user data; and    -   the UE's processing circuitry is configured to execute a client        application associated with the host application.-   D12. A method implemented in a communication system including a host    computer, a base station and a user equipment (UE), the method    comprising:    -   at the host computer, providing user data; and    -   at the host computer, initiating a transmission carrying the        user data to the UE via a cellular network comprising the base        station, wherein the UE performs any of the steps described for        the Group A embodiments.-   D13. The method of embodiment D12, further comprising at the UE,    receiving the user data from the base station.-   D14. A communication system including a host computer comprising:    -   communication interface configured to receive user data        originating from a transmission from a user equipment (UE) to a        base station,    -   wherein the UE comprises a radio interface and processing        circuitry, the UE's processing circuitry configured to perform        any of the steps described for the Group A embodiments.-   D15. The communication system of embodiment D14, further including    the UE.-   D16. The communication system of any of embodiments D14 through D15,    further including the base station, wherein the base station    comprises a radio interface configured to communicate with the UE    and a communication interface configured to forward to the host    computer the user data carried by a transmission from the UE to the    base station,-   D17. The communication system of any of embodiments D14 through D16,    wherein:    -   the processing circuitry of the host computer is configured to        execute a host application; and    -   the UE's processing circuitry is configured to execute a client        application associated with the host application, thereby        providing the user data.-   D18. The communication system of any of embodiments D14 through D17,    wherein:    -   the processing circuitry of the host computer is configured to        execute a host application, thereby providing request data; and    -   the UE's processing circuitry is configured to execute a client        application associated with the host application, thereby        providing the user data in response to the request data.-   D19. A method implemented in a communication system including a host    computer, a base station and a user equipment (UE), the method    comprising:    -   at the host computer, receiving user data transmitted to the        base station from the UE, wherein the UE performs any of the        steps described for the Group A embodiments.-   D20. The method of embodiment D19, further comprising, at the UE,    providing the user data to the base station.-   D21. The method of any of embodiments D19 through D20, further    comprising:    -   at the UE, executing a client application, thereby providing the        user data to be transmitted; and    -   at the host computer; executing a host application associated        with the client application.-   D22. The method of any of embodiments D19 through D21, further    comprising:    -   at the UE, executing a client application; and    -   at the UE, receiving input data to the client application, the        input data being provided at the host computer by executing a        host application associated with the client application,    -   wherein the user data to be transmitted is provided by the        client application in response to the input data.-   D23. A user equipment (UE) configured to communicate with a base    station, the UE comprising a radio interface and processing    circuitry configured to perform the method of any of embodiments D19    through D22.-   D24. A communication system including a host computer comprising a    communication interface configured to receive user data originating    from a transmission from a user equipment (UE) to a base station;    wherein the base station comprises a radio interface and processing    circuitry, the base station's processing circuitry configured to    perform any of the steps described for the Group B embodiments.-   D25. The communication system of embodiment D24 further including    the base station.-   D26. The communication system of any of embodiments D24 through D25,    further including the UE, wherein the UE is configured to    communicate with the base station.-   D27. The communication system of any of embodiments D24 through D25,    wherein:    -   the processing circuitry of the host computer is configured to        execute a host application;    -   the UE is configured to execute a client application associated        with the host application, thereby providing the user data to be        received by the host computer.-   D28. A method implemented in a communication system including a host    computer, a base station and a user equipment (UE), the method    comprising:    -   at the host computer, receiving, from the base station, user        data originating from a transmission which the base station has        received from the UE, wherein the UE performs any of the steps        described for the Group A embodiments.-   D29. The method of embodiment D28, further comprising at the base    station, receiving the user data from the UE.-   D30. The method of any of embodiments D28 through D29, further    comprising at the base station, initiating a transmission of the    received user data to the host computer.-   D31. A method implemented in a communication system including a host    computer, a base station and a user equipment (UE), the method    comprising:    -   at the host computer, receiving, from the base station, user        data originating from a transmission which the base station has        received from the UE, wherein the base station performs any of        the steps described for the Group B embodiments.-   D32. The method of embodiment D31, further comprising at the base    station, receiving the user data from the UE.-   D33. The method of any of embodiments D31 through D32, further    comprising at the base station, initiating a transmission of the    received user data to the host computer.

The invention claimed is:
 1. A method for a transmitter apparatusconfigured to transmit signals to a receiver apparatus using atransmission beam selected from a plurality of available transmissionbeams, wherein the receiver apparatus is configured to receive thesignals using a reception beam selected from a plurality of availablereception beams, and wherein a set of the available transmission beamsand a set of the available reception beams are for beam selectionmeasurements by the receiver apparatus, the method comprising:determining a collection of linear combinations of transmission beams ofthe set of the available transmission beams; determining a collection oflinear combinations of reception beams of the set of available receptionbeams; providing an indication of the collection of linear combinationsof reception beams to the receiver apparatus; and transmitting each ofthe linear combinations of transmission beams of the collection oflinear combinations of transmission beams for beam selectionmeasurements by the receiver apparatus.
 2. The method of claim 1,wherein the collection of linear combinations of transmission beams andthe collection of linear combinations of reception beams are determinedjointly.
 3. The method of claim 1, wherein: a cardinality of thecollection of linear combinations of transmission beams is lower than acardinality of the set of the available transmission beams; and/or acardinality of the collection of linear combinations of reception beamsis lower than a cardinality of the set of the available reception beams.4. The method of claim 3, wherein the determination of the collection oflinear combinations of transmission beams and the collection of linearcombinations of reception beam comprises determining the cardinality ofthe collection of linear combinations of transmission beams and/or thecardinality of the collection of linear combinations of reception beambased on one or more of: a sparsity of a channel between the transmitterapparatus and the receiver apparatus; and properties of a compressionmatrix representing the collection of linear combinations oftransmission beams and the collection of linear combinations ofreception beams.
 5. The method of claim 1, further comprising: receivinga transmission beam selection measurement report from the receiverapparatus; and selecting the transmission beam from the plurality ofavailable transmission beams in accordance with the receivedtransmission beam selection measurement report.
 6. The method of claim1, wherein at least one of the linear combinations of transmission beamsof the collection of linear combinations of transmission beams is alinear combination of at least two of the transmission beams of the setof the available transmission beams, and/or wherein at least one of thelinear combinations of reception beams of the collection of thecollection of linear combinations of reception beams is a linearcombination of at least two of the reception beams of the set of theavailable reception beams.
 7. The method of claim 1, wherein each of thelinear combinations of transmission beams of the collection of linearcombinations of transmission beams is a unique linear combination of allof the transmission beams of the set of the available transmissionbeams, and/or wherein each of the linear combinations of reception beamsof the collection of the collection of linear combinations of receptionbeams is a unique linear combination of all of the reception beams ofthe set of the available reception beams.
 8. The method of claim 1,wherein the collection of linear combinations of transmission beams isdefined by a Grassmannian coding matrix, and/or wherein the collectionof linear combinations of reception beams is defined by a Grassmanniancoding matrix.
 9. The method of claim 1, wherein the collection oflinear combinations of transmission beams, representable by a matrixB_(TX), and the collection of linear combinations of reception beams,representable by a matrix B_(RX), are determined such that A^(H)A is asubstantially block diagonal matrix, wherein A=B_(TX)⊗B_(RX) where ⊗represents a Kronecker product.
 10. The method of claim 1, wherein theset of the available transmission beams consists of a minimum number oftransmission beams spanning the plurality of available transmissionbeams, and/or wherein the set of the available reception beams consistsof a minimum number of reception beams spanning the plurality ofavailable reception beams.
 11. The method of claim 1, wherein the set ofthe available transmission beams and/or the set of the availablereception beams comprises discrete Fourier transform, DFT, beams,wherein a beam direction of any DFT beam corresponds to a harmonicfrequency.
 12. The method of claim 1, wherein transmitting comprises oneor more of: transmitting each of the linear combinations of transmissionbeams of the collection of linear combinations of transmission beams ina respective transmission time resource, at least some of the respectivetime resources being different; and transmitting each of the linearcombinations of transmission beams of the collection of linearcombinations of transmission beams in a respective transmissionfrequency resource, at least some of the respective frequency resourcesbeing different.
 13. The method of claim 1, wherein the method isapplied during a training phase for beam selection.
 14. A method for areceiver apparatus configured to receive signals from a transmitterapparatus via a transmission beam selected from a plurality of availabletransmission beams and using a reception beam selected from a pluralityof available reception beams, wherein a set of the availabletransmission beams and a set of the available reception beams are forbeam selection measurements by the receiver apparatus, the methodcomprising: acquiring, from the transmitter apparatus, an indication ofa collection of linear combinations of reception beams of the set of theavailable reception beams; receiving, using each of the linearcombinations of reception beams of the collection of linear combinationsof reception beams, a number of measurement signals for beam selectionmeasurements from the transmitter apparatus, wherein the number ofmeasurement signals correspond to a collection of linear combinations oftransmission beams of the set of available transmission beams; andperforming beam selection measurements on the number of measurementsignals for selection of the transmission beam from the plurality ofavailable transmission beams and for selection of the reception beamfrom the plurality of available reception beams.
 15. The method of claim14, further comprising: transmitting a transmission beam selectionmeasurement report to the transmitter apparatus for selection of thetransmission beam from the plurality of available transmission beams.16. The method of claim 14, wherein performing beam selectionmeasurements comprises determining a quality metric for each combinationof a transmission beam of the set of available transmission beams and areception beam of the set of available reception beams based on the beamselection measurements.
 17. The method of claim 14, wherein performingbeam selection measurements comprises subjecting the number of receivedmeasurement signals to matched filtering based on the collection oflinear combinations of transmission beams and the collection of linearcombinations of reception beam.
 18. A method for a system comprising atransmitter apparatus and a receiver apparatus, wherein the transmitterapparatus is configured to transmit signals to the receiver apparatususing a transmission beam selected from a plurality of availabletransmission beams, wherein the receiver apparatus is configured toreceive the signals using a reception beam selected from a plurality ofavailable reception beams, and wherein a set of the availabletransmission beams and a set of the available reception beams are forbeam selection measurements by the receiver apparatus, the methodcomprising: determining, by the transmitter apparatus, a collection oflinear combinations of transmission beams of the set of the availabletransmission beams; determining, by the transmitter apparatus, acollection of linear combinations of reception beams of the set ofavailable reception beams; providing, by the transmitter apparatus tothe receiver apparatus, an indication of the collection of linearcombinations of reception beams; acquiring, by the receiver apparatusfrom the transmitter apparatus, the indication of the collection oflinear combinations of reception beams; transmitting, by the transmitterapparatus, each of the linear combinations of transmission beams of thecollection of linear combinations of transmission beams; receiving, bythe receiver apparatus, each of the linear combinations of transmissionbeams of the collection of linear combinations of transmission beamsusing each of the linear combinations of reception beams of thecollection of linear combinations of reception beams; and performing, bythe receiver apparatus, beam selection measurements on the receivedlinear combinations of transmission beams for selection of thetransmission beam from the plurality of available transmission beams andfor selection of the reception beam from the plurality of availablereception beams.
 19. A computer program product comprising anon-transitory computer readable medium, having thereon a computerprogram comprising program instructions, the computer program beingloadable into a data processing unit and configured to cause executionof a method when the computer program is run by the data processingunit, wherein the method is for a transmitter apparatus configured totransmit signals to a receiver apparatus using a transmission beamselected from a plurality of available transmission beams, wherein thereceiver apparatus is configured to receive the signals using areception beam selected from a plurality of available reception beams,and wherein a set of the available transmission beams and a set of theavailable reception beams are for beam selection measurements by thereceiver apparatus, and wherein the method comprises: determining acollection of linear combinations of transmission beams of the set ofthe available transmission beams; determining a collection of linearcombinations of reception beams of the set of available reception beams;providing an indication of the collection of linear combinations ofreception beams to the receiver apparatus; and transmitting each of thelinear combinations of transmission beams of the collection of linearcombinations of transmission beams for beam selection measurements bythe receiver apparatus.
 20. A transmitter apparatus configured totransmit signals to a receiver apparatus using a transmission beamselected from a plurality of available transmission beams, wherein thereceiver apparatus is configured to receive the signals using areception beam selected from a plurality of available reception beams,and wherein a set of the available transmission beams and a set of theavailable reception beams are for beam selection measurements by thereceiver apparatus, the apparatus comprising controlling circuitryconfigured to cause: determination of a collection of linearcombinations of transmission beams of the set of the availabletransmission beams; determination of a collection of linear combinationsof reception beams of the set of available reception beams; provision ofan indication of the collection of linear combinations of receptionbeams to the receiver apparatus; and transmission of each of the linearcombinations of transmission beams of the collection of linearcombinations of transmission beams for beam selection measurements bythe receiver apparatus.
 21. The transmitter apparatus of claim 20,wherein the controlling circuitry is configured to cause jointdetermination of the collection of linear combinations of transmissionbeams and the collection of linear combinations of reception beams. 22.The transmitter apparatus of claim 20, wherein: a cardinality of thecollection of linear combinations of transmission beams is lower than acardinality of the set of the available transmission beams; and/or acardinality of the collection of linear combinations of reception beamsis lower than a cardinality of the set of the available reception beams.23. The transmitter apparatus of claim 22, wherein the controllingcircuitry is configured to cause the determination of the collection oflinear combinations of transmission beams and the collection of linearcombinations of reception beam by causing determination of thecardinality of the collection of linear combinations of transmissionbeams and/or the cardinality of the collection of linear combinations ofreception beam based on one or more of: a sparsity of a channel betweenthe transmitter apparatus and the receiver apparatus; and properties ofa compression matrix representing the collection of linear combinationsof transmission beams and the collection of linear combinations ofreception beams.
 24. The transmitter apparatus of claim 20, wherein thecontrolling circuitry is further configured to cause: reception of atransmission beam selection measurement report from the receiverapparatus; and selection of the transmission beam from the plurality ofavailable transmission beams in accordance with the receivedtransmission beam selection measurement report.
 25. The transmitterapparatus of claim 20, wherein the controlling circuitry is configuredto cause the transmission by causing one or more of: transmission ofeach of the linear combinations of transmission beams of the collectionof linear combinations of transmission beams in a respectivetransmission time resource, at least some of the respective timeresources being different; and transmission of each of the linearcombinations of transmission beams of the collection of linearcombinations of transmission beams in a respective transmissionfrequency resource, at least some of the respective frequency resourcesbeing different.
 26. The transmitter apparatus of claim 20, wherein thecontrolling circuitry is configured to enable the determination of thecollections, the provision of the indication, and the transmission ofthe linear combinations of transmission beams for application during atraining phase for beam selection.
 27. A receiver apparatus configuredto receive signals from a transmitter apparatus via a transmission beamselected from a plurality of available transmission beams and using areception beam selected from a plurality of available reception beams,wherein a set of the available transmission beams and a set of theavailable reception beams are for beam selection measurements by thereceiver apparatus, the apparatus comprising controlling circuitryconfigured to cause: acquisition, from the transmitter apparatus, of anindication of a collection of linear combinations of reception beams ofthe set of the available reception beams; reception, using each of thelinear combinations of reception beams of the collection of linearcombinations of reception beams, of a number of measurement signals forbeam selection measurements from the transmitter apparatus, wherein thenumber of measurement signals correspond to a collection of linearcombinations of transmission beams of the set of available transmissionbeams; and performance of beam selection measurements on the number ofmeasurement signals for selection of the transmission beam from theplurality of available transmission beams and for selection of thereception beam from the plurality of available reception beams.
 28. Thereceiver apparatus of claim 27, wherein the controlling circuitry isfurther configured to cause: transmission of a transmission beamselection measurement report to the transmitter apparatus for selectionof the transmission beam from the plurality of available transmissionbeams.
 29. The receiver apparatus of claim 27, wherein the controllingcircuitry is configured to cause performance of beam selectionmeasurements by causing determination of a quality metric for eachcombination of a transmission beam of the set of available transmissionbeams and a reception beam of the set of available reception beams basedon the beam selection measurements.
 30. The receiver apparatus of claim27, wherein the controlling circuitry is configured to cause performanceof beam selection measurements by causing subjection of the number ofreceived measurement signals to matched filtering based on thecollection of linear combinations of transmission beams and thecollection of linear combinations of reception beam.
 31. A network nodecomprising the transmitter apparatus of claim
 20. 32. A wirelesscommunication device comprising the transmitter apparatus of claim 20.33. A system comprising a transmitter apparatus and a receiverapparatus, wherein the transmitter apparatus is configured to transmitsignals to the receiver apparatus using a transmission beam selectedfrom a plurality of available transmission beams, wherein the receiverapparatus is configured to receive the signals using a reception beamselected from a plurality of available reception beams, and wherein aset of the available transmission beams and a set of the availablereception beams are for beam selection measurements by the receiverapparatus, wherein: the transmitter apparatus is configured to:determine a collection of linear combinations of transmission beams ofthe set of the available transmission beams; determine a collection oflinear combinations of reception beams of the set of available receptionbeams; provide, to the receiver apparatus, an indication of thecollection of linear combinations of reception beams; and transmit eachof the linear combinations of transmission beams of the collection oflinear combinations of transmission beams; and the receiver apparatus isconfigured to: acquire, from the transmitter apparatus, the indicationof the collection of linear combinations of reception beams; receiveeach of the linear combinations of transmission beams of the collectionof linear combinations of transmission beams using each of the linearcombinations of reception beams of the collection of linear combinationsof reception beams; and perform beam selection measurements on thereceived linear combinations of transmission beams for selection of thetransmission beam from the plurality of available transmission beams andfor selection of the reception beam from the plurality of availablereception beams.
 34. A network node comprising the receiver apparatus ofclaim
 27. 35. A wireless communication device comprising the receiverapparatus of claim 27.